Michelle Pfeiffer and Alec Baldwin in Married to the Mob. Photo: Orion/Kobal/REX/Shutterstock

When Jonathan Demme died last April at the age of 73, it wasn’t particularly easy to sum up a directorial career that began with Caged Heat, the quintessential women-in-prison exploitation movie, and ended with the concert film Justin Timberlake + The Tennessee Kids. That’s partially because of the range suggested by those bookends, but also because of the films themselves, which are never quite what they look like from the outside. Or, more accurately, they also contain more than they look like they’ll contain from a distance.

Caged Heat, for instance, folds a subversive streak and a gift for cleverly staged set pieces into the expected elements of a Roger Corman drive-in movie. Like Demme’s beloved Stop Making Sense, Justin Timberlake + The Tennessee Kids is a concert film that doubles as a story about staging the show itself and the communal effort required for such a show to happen. Demme didn’t just always deliver, he always over-delivered in the best possible sense.

That’s never more evident than in Married to the Mob, released in 30 years ago this month at the tail end of a diverse summer movie season that included Die Hard, Coming to America, Big, Bull Durham, and Midnight Run. It wasn’t a bad summer for movies, in other words, but, then as now, August tended to be a home for oddball movies that didn’t quite fit anywhere else, released with fingers crossed that they might catch fire as the summer wound down. In bare description, Married to the Mob fits the profile of an August movie. And despite a clever script by Barry Strugatz and Mark R. Burns, in another director’s hands it could have been just one of many ’80s movies, inspired by the success of Beverly Hills Cop, to mix action and crime and hope for the best.

But Demme wasn’t just any director. He was always looking for ways to go deeper, to squeeze a little bit more into each frame, to capture the telling gestures that defined a character, to get a little more out of every moment. Sometimes that involved savvy, counterintuitive casting. Anyone else’s list of late-’80s actresses born to play an Italian-American Long Islander with ties to the Mafia (and an accent that made no secret of it) probably wouldn’t have included Michelle Pfeiffer. A California-born blonde, Pfeiffer had mostly been seen in parts that matched that description, never quite finding the breakout starring role she deserved. Here, from her first moment, Pfeiffer makes it clear this will be that role.

Demme introduces her sitting in a hair salon with her back to a bevy of other mob wives. She can’t hear them gossiping about her stuck-up ways, but she can hear her hairdresser, Ray, praising her follicles. Yet this brings Pfeiffer’s Angela de Marco no joy. When Ray spins her around, she looks gripped by despair, like a woman whose life has taken her somewhere she’d never wish to be. “You don’t like it?” he asks. “No, no,” she assures him. “It’s not the cut.” The opening credits, which pair Rosemary Clooney’s “Mambo Italiano” to preparations for a mob hit, have already set up that Married to the Mob will be a comedy about colorful gangsters running afoul of the law. But it’s the way Pfeiffer delivers that line that gives the movie its soul.

While the others revel in all the luxury ill-gotten wealth can buy in the New York suburbs — Joan Cusack’s character sports an especially fetching lion-cub brooch — Angela can barely hide her discontent. The plot will soon leave her a widow when capo Tony “the Tiger” Russo (Dean Stockwell, in a performance that earned him a Best Supporting Actor nomination) takes out Angela’s husband, Frank “the Cucumber” de Marco (Alec Baldwin), in a jealous rage. But Angela has already been set up as a woman apart. So the widow de Marco gives away her possessions, grabs her son (who’s started running three-card monte games in their backyard), and heads to Manhattan’s Lower East Side, still a neighborhood defined more by low-rent apartments, diverse residents, and funky little businesses than Duane Reades — the kind of place where someone could forget their past and reinvent themselves for a better tomorrow.

At its heart, Married to the Mob is a story of reinvention, one in which a woman flees the stifling conformity of the suburbs for the possibilities of the city. In one memorable scene, Angela finds herself at the supermarket pinned in by the shopping carts of the other wives, headed by Tony’s insanely jealous spouse Connie (Mercedes Ruehl), who’s become aware that Angela has captured her husband’s eye. It’s funny, but it’s also the most frightening cinematic shopping trip this side of The Stepford Wives. But even without the threat of ostracism (or worse), Angela knows she can’t stay, and so trades in a house full of stolen luxury items for a crappy apartment with a bathtub in the kitchen and a job helping out at the Hello Gorgeous beauty salon managed by a Jamaican immigrant named Rita (reggae artist and Demme regular Sister Carol), who gives her a shot — and a haircut that finally makes her smile.

In some ways, Married to the Mob works almost like a Mafia operation itself: The colorful gangsters with their bad tempers and worse taste serve as a front for a different, deeper sort of story. Which isn’t to say that Demme doesn’t supply the action-comedy goods promised by the film’s upbeat trailer. (A trailer set in part to New Order’s “Bizarre Love Triangle”; the eclectic, ahead-of-the-curve soundtrack, another Demme trademark, includes everyone from the Pixies to Ziggy Marley to Sinead O’Connor to Demme’s favorite band, the Feelies.) Demme makes the mob’s corner of Long Island into a tacky wonderland, and moves the finale to Miami for a tropical variation of the same aesthetic, and the film maintains a real sense of danger from beginning to end, interrupting laughs with jolting moments of violence. Then there’s the cast. With a squint that instantly conveys the mix of cunning and ruthlessness that’s allowed him to rise to the top, Stockwell’s at once amusing and threatening. As the FBI agent who falls for Angela while surveilling her, Matthew Modine is as charming as he is goofy, a man so square and forthright that his virtue becomes its own sort of eccentricity.

But it’s Ruehl who threatens to steal the movie whenever she’s onscreen. Where Angela internalizes her unhappiness, Ruehl’s Connie seems only to have an external life, expressing whatever emotion is roiling though her at any given moment and pivoting from affection to murderous rage in an instant. That supermarket confrontation with Angela ends with Connie crushing a carton of eggs with her hands, a gesture that shifts from hilarious to threatening to sad. In her own way, Connie’s just as troubled by an aching dissatisfaction as Angela, and even her most over-the-top gestures are from the heart.

That’s true of all of Married to the Mob, in which Demme sticks to a cartoonish premise while also crafting a story of a woman finding herself again. And ultimately, more than any visual signature of thematic obsession, it’s that deep investment in what’s beneath the surface of his films that defines the Demme touch. I’m not sure any film captures that touch better than Married to the Mob, even if it usually gets mentioned behind titles like Melvin and Howard, Philadelphia, Stop Making Sense, Silence of the Lambs, and Married to the Mob’s 1986 companion piece Something Wild in discussions of his best films. It’s loose and breezy and fun and packed with colorful characters (some of whom just wander in to steal a scene before departing), a light tale of crime and misadventure. But it balances all that against a soulfulness to match its protagonist’s yearning for something more. Demme delivered on the promise of the assignment, then he delivered even more. Just like he always did.