Jack Lemmon often gets referred to as the great everyman of American actors – down-to-earth, identifiable, a little put-upon but fundamentally decent. And that’s the image that gets projected when his character in The Apartment, a lowly insurance accountant named CC “Bud” Baxter, is first shown at desk #861 on the 19th floor of the Consolidated Life building in New York – a city whose population, he tells us, would stretch from “Times Square to the outskirts of Karachi” if they were laid end-to-end. What man could be more average than the one sitting among a sea of office drones so expansive that they work from 8.50am to 5.20pm, every day, just to stagger the elevator times?

Still an indefinable marvel after 60 years, The Apartment is not merely about an everyman type, but a profound reflection on what life is like for the everyman in America – and for the everywoman, too, as embodied by Shirley MacLaine, playing Fran Kubelik, a lowly elevator operator. Director Billy Wilder, operating at the peak of his powers – he and his screenwriting partner IAL Diamond had made the screwball classic Some Like It Hot with Lemmon one year earlier – has made a comedy about two people who are utterly compromised and in no control over their own lives and happiness. He has also made a heartrending drama about the same thing. And then, finally, as a small and precious mercy to Bud, Fran, and the audience that’s come to love them, he’s made a little bit of romance, too.

The premise for The Apartment, inspired in part by Noël Coward’s Brief Encounter, sounds like the type of broad bedroom farce that Wilder handled so deftly in Some Like It Hot and The Seven Year Itch. Bud is a hard-working bachelor whose combination of career ambition, deference, and low self-esteem has led him to loan out his Manhattan apartment to company executives who need a place to take their mistresses. With four bosses already on the schedule – and the biggest boss of all, Mr Sheldrake (Fred MacMurray), bidding to be the fifth – Bud spends most nights shut out of his own place. A typical evening finds him cooking a sad TV dinner for himself at 9pm, and an atypical evening sends him out to Central Park after midnight to accommodate a spontaneous one-night stand.

For Bud, the carrot dangling at the end of this stick is the promotion his betters have promised him, which finally arrives in the form of a second administrative assistant job that could not sound more deflating, but comes with an office door with stenciled letters. He flirts with Fran in the elevator – she appreciates that he takes off his hat, like a gentleman – but the notion that he could ever take a woman back to his own apartment, like his bosses do, seems utterly fanciful, as if only top-level executives deserve to get lucky. As it turns out, Fran is having an affair with Mr Sheldrake, the latest in a long line of pretty office ladies who accept the fiction that Sheldrake will leave his wife and family in White Plains when the time is right. The relationship will end, as the others did, when the lie becomes too embarrassingly obvious.

Wilder and Diamond wring all the laughs they can out of this idea, particularly in a masterly sequence where Bud catches a cold and works frantically at his desk to rearrange schedules so he can recuperate at home. (Sheldrake proves not to be flexible.) But what’s surprising about The Apartment is how far it steers into outright despair – though even that, in the true Wilder spirit, isn’t unleavened despair. When Fran finally comes to the inevitable realization about Sheldrake, on a night he’s taken her to Bud’s apartment for a casual romp, she takes enough sleeping pills to kill herself. After he and a neighboring doctor revive her, Bud tells his own story about a botched suicide attempt – an anecdote he’s spun generously for laughs.

Wilder is understood as a cynic about human nature, based on the greed and moral corruption on display in films like Double Indemnity and Ace in the Hole, but he always had a strong affinity for the little guy – and, in Bud and Fran, he’s found the littlest. The Apartment is a romantic comedy where the two leads are kept apart partially by circumstance and partially by the mutual understanding that they don’t deserve love. It’s inconceivable to Bud that a man of his station could attract a woman like Fran; it’s inconceivable to Fran that a woman of her station is worthy of kindness and decency. These are not typical romcom obstacles. These are two psychologically bruised individuals, conditioned to believe the key to happiness is as exclusive as the key to the executive washroom.

The tonal wizardry of The Apartment is often miraculous, like the Christmas party where Fran’s heartbreak over hearing of Sheldrake’s past dalliances contrasts directly with Bud goofing around in a new bowler hat like Charlie Chaplin. Most films define themselves as one genre or another, but this one can be several of them at once. But that sort of high-level plate-spinning is true of the screenplay in general, which is immensely satisfying in the way it keeps planting and paying off turns of the plot. When Bud discovers a broken compact mirror left in his apartment and returns it to Sheldrake, we know that it belongs to Fran but he doesn’t; when Fran allows Bud to use it during the party, it’s a reveal that crushes his spirit. Other seeds sprout later, too, like the keys that circulate the office or sleeping pills that take on different meanings in different contexts. A Wilder and Diamond screenplay can make the whole field seem like a lost art.

And finally, there’s Jack Lemmon and Shirley MacLaine. Fran may be more glamorous than the lowly Bud, but Lemmon and MacLaine keep them on the same wavelength – courteous and deferential to a fault, yet high-spirited and silly by nature, trading the sort of elevated banter that tends to separate the couples in old screwball comedies from mere mortals. It’s so obvious to the audience that they belong together, and so elating when it finally happens – as it should be in any good romcom. But The Apartment understands the forces that keep them apart so clearly, and they’re as ordinary as clocking into work.