The blunt opening title card of “Shining Vale” feels like a test: “Women are twice as likely as men to suffer from depression,” it reads, seeming to signal the beginning of a clunky show about Women and Depression — at least until the next sentence appears onscreen. “Women are also twice as likely to be possessed by a demon,” it says, a immediate and deliberate wink of self-awareness at an audience that might’ve already tried to write the show off. What’s more, it adds: “the symptoms are the same.”

Throughout the first seven episodes made available for critics (the season will have eight in total), “Shining Vale” follows a Brooklyn family coming to grips with the inherent strangeness of their new Connecticut home to increasingly catastrophic ends. It also ends up juggling so many tricky narrative plates — depression, generational trauma, the slow and steady awakening of a haunted house — that they could easily all come crashing to the ground. And yet, even in the moments when that possibility seems perilously close, the wrinkles still feel a part of the show’s overall tapestry. Perhaps most importantly: “Shining Vale” has a honed sense of humor, usually (and especially) when it’s least expected.

This isn’t a complete shock given the cast and crew behind the new Starz series, co-created by Jeff Astrof (“Trial and Error”) and Sharon Horgan (“Catastrophe”). As Pat, a former wild child turned author, Courteney Cox finds a role worthy of her singular ability to make any frustrated sentence a comedic exclamation point. She also gets solid foils to play off, between Greg Kinnear as Pat’s well-meaning but rather clueless husband, Terry; Merrin Dungey as her prickly agent; Judith Light as her formerly institutionalized mother; and Mira Sorvino as the glamorous 1950s housewife who refuses to stop haunting her. Even Pat and Terry’s teenaged children get embodied by sharp performances from Gus Birney and Dylan Gage, two actors who both stood out in recent underrated comedies (“Dickinson” and “Pen15,” respectively). It only stands to reason that this cast can handle the combination of Astrof’s farcical banter and Horgan’s acidic bite.

What’s more surprising about “Shining Vale” is how it ably counterbalances the writing’s comedic throughline with genuinely creepy touches of horror that might feel familiar to fans of the earlier, most effective seasons of “American Horror Story.” Though Pat finds it hard to trust her own instincts — especially now that she’s at the age her mother was when she experienced her worst mental health crisis — the house’s true nature can’t hide for long. As directed in the initial outings by Darbhla Walsh (“Fargo”), the series is equally as funny as it is downright chilling. Stark, wider shots of Pat and Terry’s dusty new home alternate with sudden close-ups to punctuate both thrills of terror and surprising punchlines. Jump scares are used sparingly (much to this wimp’s relief), but effectively (much to this wimp’s chagrin). While Sorvino embraces her otherworldly role with a silken smirk, eerie guest turns from Susan Park and “Twin Peaks” standout Sherilyn Fenn further emphasize her character’s grip on this unfolding nightmare. As Pat descends deeper into her own paranoia and also into the house’s history, “Shining Vale” falls down the rabbit hole with her, twisting its shape to fit whichever genre the moment calls for. (Just as in the show’s most obvious inspiration, all work and no play makes Pat a dull girl, etc.)

As for that dire, dual warning of possession being confused for depression and vice versa: the show doesn’t shy away from exploring the thorny tangle of women with mental illness struggling to understand themselves or make others understand. Its use of the haunted house as a metaphor for women who feel as trapped and conflicted as Pat, her mother, and her ghost is blatant but purposeful, as evidenced by the fact that it includes an episode literally named, “The Yellow Wallpaper.” As Pat and the series wind further down this particular road, they both threaten to get caught up in the intoxicating possibilities of its spiky drama and lose their ways. But even in these fuzzier moments, it’s hard to deny the show another chance to lure you along when the payoff is so much more often a worthwhile surprise.

“Shining Vale” premieres Sunday, March 6 at 10 pm on Starz.