NEW YORK — Hank Moody, the hero of Showtime’s comedy “Californication,” is a roguish struggling novelist who says whatever is on his mind and feels a tug from every member of the opposite sex.

He might get into less trouble if he kept his lip buttoned and his fly zipped. But that wouldn’t be Hank, nor would it be “Californication,” which mines laughs (and, occasionally, gasps) from Hank’s erotic misadventures, and those of his sexed-up fellow travelers.

Starring David Duchovny, “Californication” begins its third season Sunday at 10 p.m. with Hank landing a much-needed teaching job at a local college. This is thanks to a professor who is the sexy mother of a friend of Hank’s teenage daughter Becca (Madeleine Martin).

Here in academia, Hank is primed to seduce his new colleague (whose husband, the dean of the college, is his boss), while a graduate assistant and a sassy coed are also on Hank’s radar.

Clad smart but un-starlike in a sweater and cords, the 49-year-old Duchovny is meeting a reporter at a luncheonette on the Upper East Side, where he lives with actress Tea Leoni, his wife of a dozen years, and their two children.

In midsentence, he spies a hand-lettered sign above the vintage soda fountain.

“They have banana splits!” he says. “I got to tell the kids about that.”

These days, Duchovny’s family is together and stronger than ever, he’s happy to report.

“Things are great,” he sums up, sharing details from a cross-country RV trip they made this summer after shooting wrapped on “Californication.” Highlights: Grand Canyon, a ballgame in St. Louis and a visit with an Amish family in Ohio.

Consider: “Californication” isn’t really a show about sex, Duchovny says, but about a man with inner conflicts and self-esteem problems. Hank is a charismatic but troubled man who wants to reunite with his loved ones (Becca and her mother, Karen, played by Natascha McElhone), no matter how much his bad-boy behavior continues to drive his family apart.

“What’s funny to me is not what the character wants,” Duchovny says, “but what he can’t help doing.”

What Hank can’t help doing, and does — a lot of it — is make use of the latitude a premium-cable network like Showtime can offer its shows. “Californication” is as racy as it is funny.

And not just for Hank. This season, his agent Charlie (Evan Handler) has bawdy clashes with estranged wife Marcy (Pamela Adlon) as well as with a new boss, played by Kathleen Turner with hilarious lechery.

Not about sex, David?

“I will sometime have arguments with (series creator) Tom Kapinos,” Duchovny concedes, “and I’ll sound like an old biddy: I’ll say, ‘Why is it all about sex?’”

With a smile, he declares, “That was never the show to me.”