In movies like 2009’s Adventureland and 2011’s Bridesmaids (a picture she co-wrote), former Saturday Night Live player Kristen Wiig demonstrated not only her knack for comedy, but a barely glimpsed flair for the dramatic. And beyond the drama, there’s also been an air of sadness to Wiig’s performances. Director Craig Johnson and his cowriter, Mark Heyman (Black Swan), were smart to recognize this, fashioning their new film, The Skeleton Twins, around the actress’s hilariously melancholy talents. Fitting, for a dramatic comedy that’s built on a backbone of chronic depression.

When we first see Wiig’s Maggie, a dental hygienist living in New York’s Rockland County, she’s in her bathroom, about to swallow a fistful of pills. She’s stopped, however, by a phone call informing her that her fraternal twin, Milo, has just attempted to end his life, as we’ve already learned from the blood mixing with the water in his bathtub during the movie’s opening scene.

As good as Wiig is in the film, the real revelation is her longtime SNL cast mate Bill Hader, who plays Milo, a self-described “tragic gay cliché” who hasn’t seen his sibling in a decade. It would be easy to dismiss Hader’s performance as a feature-length version of his “Stefon” character from the late-night sketch show, but there’s a depth to Milo that cuts deeper than that flamboyant club-kid caricature—certainly deeper than the slits Milo carved in his wrists—although some of Stefon’s gleefully warped sensibility surfaces in Milo’s suicide note, which reads, “To whom it may concern: see you later,” punctuated with a smiley face.

And really, that about sums up the tone of the film; the script from old college friends Johnson and Heyman goes into some dark corners, but it always emerges in a happier place. Mind you, this undercuts the movie’s resolution, but if it’s emotional catharsis you want, it’s catharsis you’ll get. You’ll get a bellyful of laughs, too. And really, isn’t that what most people want from a film headlining the SNL veterans?

So, after Maggie travels out to Los Angeles to be there for her estranged brother, the comic sparks begin to fly. One can surmise that they’d have an easy rapport from having worked alongside each other on live TV for more than half a decade, but Maggie and Milo are just about the most believable siblings ever seen on the big screen.

Despite whatever drove these two apart, you believe that the reluctant Milo would be willing to return to the East Coast with Maggie, since the history they share is palpable. These are damaged people, but you sense they became damaged together—and their laughter, missing for so long, becomes their key to coping.

Back where he began, in the town he left with dreams of making it as an actor, Milo’s loath to admit that his ambition has led him to waiting tables at “a shitty tourist restaurant in Hollywood.” Instead, when he runs into Rich (Ty Burrell, humanizing a tricky role), his former high school English teacher, Milo informs him he’s “here for a writer’s retreat.” But really, he’s returned to try to rekindle the secret, inappropriate relationship that nearly destroyed teacher and student years before.

Secrets are something the siblings share. Maggie might have been saved from a fatal overdose when a ringing phone interfered, but she had managed to swallow some pills—of the birth control variety—which would come as a big surprise to her supportive blue-collar husband, Lance (Luke Wilson), who believes they’ve been trying to have a baby for two years.

Lance is “like a big Labrador retriever,” Milo observes, and the big lug is as naively happy as one, oblivious to his wife’s blossoming infidelity with her Aussie scuba instructor (Boyd Holbrook).

“I know. It sounds like a porno,” Maggie tells Milo when they finally begin to reconnect over hits of nitrous oxide taken after-hours at her office. “He doesn’t deserve a whore as a wife,” she concludes.

“You’re not a whore,” Milo interjects. “You’re a restless housewife with whore-like tendencies.” That’s a funny line, but the real comic highlight comes when the two drunkenly lip synch to Starship’s “Nothing’s Gonna Stop Us Now.” It’s one of those Movie Moments that should feel forced, with Johnson indulging his performers, holding on this seemingly improvised bit for the song’s duration. However, it feels right, and true; this is what Maggie and Milo would do, and in the hands of Wiig and Hader, it organically subverts cliché, instead becoming transcendent.

Save for a perfectly modulated, vulnerable speech Hader makes concerning Milo’s belief that he peaked in high school, the rest of the film remains fairly earthbound, filled with less-than-revealing details like a missing mother (Joanna Gleason, working wonders in an underwritten role) and a dead father.

Despite dipping into formula, The Skeleton Twins still pulls off the miracle of remaining funny while honestly dealing with the subject of depression. It’s those who are closest who are capable of hurting each other the most, and as much as Milo and Maggie might try to sabotage everything good and stable in their lives, it’s their laughter that guides them—and us—through.

The Skeleton Twins ***

Starring Kristen Wiig, Bill Hader, Ty Burrell, Luke Wilson, Boyd Holbrook and Joanna Gleason. Written by Mark Heyman and Craig Johnson. Directed by Craig Johnson. At Boston Common, Coolidge Corner and Kendall Square.