NEW YORK — In August 2000, a Time magazine cover story touting singles life displayed Sarah Jessica Parker and her three “Sex and the City” co-stars with the headline: “Who Needs a Husband?”

That question could apply, in spades, to Parker’s new HBO comedy, a piercingly honest yet droll exploration of a marriage on the rocks titled, brazenly, “Divorce.”

Premiering Sunday at 10 p.m. EDT, “Divorce” returns Parker to series TV in a role that will inevitably be judged against her “Sex and the City” portrayal as self-described “sexual anthropologist” Carrie Bradshaw.

But, odds are, only fleetingly. “Divorce” reintroduces the actress as Frances, a suburban wife and mother gazing into the bathroom mirror in the series’ first scene as if to wish away encroaching signs of age, whereupon husband Robert (co-star Thomas Haden Church) interrupts to beef about how Frances hogs the bathroom.

Then, his back turned to exit, Frances, fuming, flips him a bird. With that fed-up move, Parker leaves Carrie Bradshaw far behind.

“I just improvised that,” says Parker, looking pleased. “I’m so glad they used it!”

But make no mistake, very little about “Divorce” wasn’t carefully thought out, if you believe Parker. She says she and producing partner Alison Benson spent four years crafting the show’s concept while recruiting other off-screen talent that includes series creator Sharon Horgan (already winning acclaim as a star and creator of the dark romantic comedy “Catastrophe,” available on Amazon Prime) and showrunner Paul Simms (whose credits include “The Larry Sanders Show,” ”Flight of the Conchords” and “Girls”).

Then they mobilized a supporting cast including Molly Shannon, Talia Balsam and Tracy Letts.

It all adds up to a project Parker was, well, married to — and not as an acting showcase for herself; at first, she had no plans to appear in it.

What made it so important to her?

“A lot of people I knew were at a very interesting point in their relationship,” she explains. “It’s a reckoning of where we are, versus where we thought we would be, with people contemplating affairs, having affairs, surviving affairs or with marriages destroyed. I knew women who came out of divorces feeling triumphant, and others who felt it wasn’t at all like they thought the liberation would be.”

True, Parker, 51, has famously been wed for two decades to actor Matthew Broderick.

“But even if you’re not experiencing it, divorce is swirling around us all,” she says. “I felt strongly that this story should be told because it’s so many people’s story.”

Frances and Robert are a middle-aged, middle-class couple with two children living in New York’s Westchester County. Their marriage is sputtering yet stuck in place. Then a seismic event thrusts divorce into the picture.

Fortunately for the audience, if not for this couple, there’s no easy or quick resolution in sight, despite the series’ seemingly self-limiting, blunt title. Divorce for Frances and Robert, as for others in their social circle, can inflict itself as a protracted condition.

This would be a good time to mention that “Divorce,” while weighty, isn’t Bergmanesque, nor is it “Who’s Afraid of Virginia Woolf?” With sufficient frequency, the prism of “Divorce” refracts its raw, all-too-familiar truths into well-earned laughs. (“I am divorcing you,” Frances tells Robert in desperation. “I just got to get the kids to school first.”)

“I watch S.J.,” says her co-star Church (“Sideways,” ”Spiderman 3″), “and she’s so brilliant in her nuance and navigation of the dramatic and the comedic.”

That goes for Church, too. (“I would never try and blow your head off,” Robert volunteers in a funny-and-not-funny moment, to which Frances can only respond in kind, “Are you sure? Are you really SURE you would never try and blow my head off?”)

“Comedy and drama, I don’t prepare for them any different,” says Church. “I just want to make it as believable as possible, with always a sense of unknowing for the character: ‘What the (heck) is going to happen next?’ Just trying to keep it all honest. But hidden.”

Parker describes this marriage as one of “bitterness and resentment wrapped up in their very being. Frances brings divorce up by saying, ‘I want to save my life while I still care about it.’ That’s it! That’s the reason the show exists.”

Clearly, this is not the fraught yet frothy world of a single girl a-loose in pre-9-11 New York City. Francis, with 20 years of marriage under her belt, is older, sadder, wiser.

Was Parker’s decision to claim as her own the Frances role a way to purge herself of her Carrie Bradshaw past?

“I don’t WANT to be done with that association,” she says. “I loved it! But I’m an actor, I always was, and now my job is to share who Frances is with the audience.”

Through six HBO seasons and two feature films, Carrie, with her goofy couture and saucy lexicon (“frenemies,” ”toxic bachelor”), helped give life to a then-new phase of women’s liberation and made “Sex and the City” a cultural marker.

“Divorce,” no less reflective of the era in which it arrives, could have a similar impact. (Who needs a marriage?)

“With this show, I think we’re initially asking more of our audience: We’re asking them to be part of combat,” says Parker. “But I think its relevance is equal to ‘Sex and the City.’ It’s just different.”

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EDITOR’S NOTE — Frazier Moore is a national television columnist for The Associated Press. He can be reached at fmoore@ap.org and at http://www.twitter.com/tvfrazier. Past stories are available at http://bigstory.ap.org/content/frazier-moore

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Online:

http://www.hbo.com/divorce

Frazier Moore, The Associated Press