A show of love for Nick Offerman and Megan Mullally

Nick Offerman races into the lobby of West Los Angeles’ Odyssey Theatre, pulls off his green trucker’s cap and wipes his brow. Megan Mullally, right behind him, smooths her magenta-tinted hair and adjusts her cat-eye glasses.

“It’s a thing with us,” Offerman says, only slightly abashed for arriving 30 minutes after rehearsal was set to begin for their new play “Annapurna.” “We’re chronically late.”

Mullally slips her arm through Offerman’s, he pecks her cheek and they exhale in tandem.

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The gesture is so in sync they burst into laughter as if under the spell of some kind of loopy love dust.

“We just like each other,” Mullally says with a girlie giggle.

Most people know Mullally and Offerman from their well-known sitcom characters — she played the shrill and self-obsessed Karen Walker on “Will & Grace”; he’s the cranky and carnivorous Ron Swanson on “Parks and Recreation.”

They are also one of Hollywood’s most enduring couples. Married nearly 10 years, they’ve been together 13 years and constantly find ways to work together. Offerman appeared as a plumber on “Will & Grace”; Mullally shows up on “Parks” as Ron’s ex-wife, the hot and evil Tammy II.

On Adult Swim’s “Childrens Hospital,” he’s Det. Briggs to her Chief. And they’re the voices behind the hippie-farmer couple on Fox’s animated “Bob’s Burgers.”

This spring, they’re in the indie film “Somebody Up There Likes Me,” which Offerman produced. They just finished shooting “Townies,” starring Seth Rogen and Zac Efron. And on May 31, they’ll appear in “The Kings of Summer,” Jordan Vogt-Roberts’ coming-of-age comedy, which opened at Sundance with the title “Toy’s House.”

Right now, they are starring in Sharr White’s “Annapurna,” directed by Bart DeLorenzo, their longtime friend, collaborator and founding artistic director of the Evidence Room.

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The two-person play, which will be at the Odyssey through June 9, is a languid, emotionally suspenseful love story about an overdue reckoning between two deeply entwined people, Emma and Ulysses, who haven’t seen each other in 20 years. Set in the Colorado mountains within the confines of a dilapidated trailer, it’s more a drama than a comedy, exploring love, addiction, the constructs of family and impending death. Yet as the story unfolds, it’s studded with funny and poignant moments.

“These are hard parts to cast,” DeLorenzo says. “You need terrific comedic actors who can also bring enormous depth, which is rare. Megan and Nick, they bring the depth of their relationship to it. They spark different reactions in each other, they inspire each other; and I knew that would add a whole other layer to the production.”

During rehearsal, there’s an almost visible electricity as their characters spar.

In the scene, which DeLorenzo calls “a really dark moment in these characters’ lives,” Emma reveals a terrible truth from their past. It couldn’t be further from Mullally and Offerman’s real life; but the depth of connection and intimacy rings true and is especially potent in the 99-seat theater, where even the back row feels as if it’s in the on-stage mobile home.

“I can’t write something about me, without it being about you!” Offerman’s character, a poet, says at one point.

“Nice, nice, very nice,” DeLorenzo says. Offerman walks to the edge of the stage for more notes, an intense, pensive look on his face.

Mullally, meanwhile, does an exaggerated chicken-dance across the stage — something of a reverse moonwalk, with her neck jutting out — to blow off steam. Offerman cracks up.

“It’s a lot of alone time together,” Mullally says later in the green room about having no other cast members. “It’s great. There are no annoying others.”

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Much needed time together is largely what lured them back to the theater. Not only has their TV and film acting kept them busy, they’re engaged in a whirl of music and writing projects. Offerman has a humor book coming out this fall and has been touring with his one-man comedy-music show, “American Ham,” which he describes as “songs and woodworking tips with minor nudity.” Mullally is co-writing a sitcom for IFC, “Two Idiots,” a broad, Laurel and Hardy-like physical comedy; and she’s been performing with her new two-person band, Nancy and Beth, with “Friday Night Lights” actress Stephanie Hunt (they met filming “Somebody Up There Likes Me”).

Mullally and Offerman’s frenzied schedules take them on and off the road separately, making them crave a slower, more singularly focused schedule — not to mention each other. “Annapurna” was a way to return to their first love, the theater. Not to mention, Offerman adds, “lockdown time — we can’t leave town.”

A DeLorenzo-produced play, “The Berlin Circle,” first brought Mullally and Offerman together in 2000. At the time, “Will & Grace” was a hit — Mullally would win her second Emmy later that year. Offerman was new to L.A. and didn’t own a TV. “I had never seen an episode of ‘Friends’ or ‘Seinfeld,’” Offerman says. “I was anti-television.”

He was also the only one in the cast, he says, who wasn’t “freaked out” by Mullally’s fame. “I went up to her and said, ‘Hey, I’m Nick. I think this is going to be a lot of fun.’”

They began an under-wraps romance that solidified during a July 4 Glen Campbell concert at the Hollywood Bowl.

“We’d been courting, but I was putting him through his paces,” Mullally says. “The orchestra was playing all these patriotic, rousing numbers. I turned to him while the fireworks were going off and said, ‘OK, you’re officially my boyfriend.’”

They got engaged a year and a half later and married in 2003.

On the surface they appear worlds apart — Mullally, wearing a white blouse and beaded choker, comes off as an arts sophisticate; Offerman typically sports more rustic attire, such as the Miller High Life T-shirt he has on today.

But they’re actually cut from the same cloth. Both were raised in Middle America — she comes from Oklahoma City, he grew up on a farm outside Chicago — and share a love of comfort food, musicals, small poodles and Tom Waits. And both describe themselves as “down home neo-luddites” who share an email address.

PHOTOS: Hollywood stars on stage

She’s passionate about interior design; he’s an accomplished woodworker who crafts furniture at his Offerman Woodshop.

Even their career arcs have been oddly parallel. Though she’s 54 and he’s 42, both spent time in Chicago’s theater scene and moved to L.A. at 26 for romances that quickly soured, both landed career-defining sitcoms at 39 and both have always found solace in the theater.

“We’re both interested in doing work that uplifts the spirit, rather than action movies,” Offerman says.

Not quite along those lines, they made DIY-style “bong videos” to virally promote “Somebody Up There Likes Me.” One video featured Amy Poehler, Adam Scott, Alison Brie and Hunt.

“It’s not the normal stuff that most couples do together,” Mullally laughs.

At the end of Offerman’s recent “American Ham” show at Largo, Mullally and Hunt as Nancy and Beth skipped out on stage. With a soft, breathy voice that so often precedes a vicious attack from one of her TV characters, Mullally cooed, “It’s not so much a song as it is kind of a poem.” The guitarist plucked a few, sweet, melodic chords. Then they smashed into a crude, profanity-filled number, a hilarious cover of a rap by Riskay.

In the upcoming “Kings of Summer,” Mullally and Offerman play grating parents, in separate families, to teen boys who escape to the woods to build their own house and live off the land. Like “Somebody Up There Likes Me,” it’s a coming-of-age story with a smart, indie sensibility.

But Offerman says he and Mullally aren’t drawn to any particular film aesthetic, “just good writing.”

“I found Chris [Galletta’s] script incredibly touching and really funny,” Offerman adds. “The director said, ‘Do you think we can get Megan Mullally?’ I said, ‘Lemme make a few calls!’”

Among Offerman’s other film projects are “We’re the Millers” with Jennifer Aniston and Diablo Cody’s directorial debut, “Paradise,” alongside Holly Hunter.

More than anything, however, he loves doing meaty acting scenes with Mullally. “The chemistry we have is similar to Ron and Tammy,” Offerman says of their “Annapurna” and “Parks” roles. “Those are the only two times we’ve ever gotten to fully engage in a complex relationship together” while acting.

“Annapurna” has so many layers,” adds Mullally. “The rhythm of how they are peeled back, how information is disseminated, the secrets revealed — that’s what ultimately sold us on it.”

Then, just to make sure things don’t get too serious, Mullally pulls out her cellphone and shows off a series of text messages from Offerman. Instead of words, there are colorful strings of Emoji images. One shows a setting sun, a taxi cab, an airplane, a rainbow and a flag.

“He’s just letting me know he’s landed,” she says in the tone of “Duh!” “It’s less cute and funnier from here. It gets into all these phallic-shaped vegetables.”

“See, part of what makes us work,” says Offerman, “is that I’m a hog and Megan is refined.”

“Humor is the glue,” Mullally says. “If we think it’s funny, we’ll pretty much do anything.”

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