Deep into “The Last Movie Stars” — a six-episode HBO Max documentary series directed by Ethan HawkePaul Newman and Joanne Woodward appear on the cover of a 1980 issue of McCall’s magazine. In the headline, his name comes first, then hers, then a reference to “their very private marriage.”

This may come as a surprise, even as the order of names, and Newman’s face forcing Woodward’s to the cover’s bottom half, make perfect sense. With movies like “Cool Hand Luke” and “The Hustler” in the canon, and Newman’s face smiling benevolently across every American salad-dressing aisle, the scope of his fame made the world see the accomplished Woodward as his wife before she was an artist. But “private”? Really? The pair’s marriage was widely discussed and covered by the press; they worked together frequently and appeared as a proto-Tom and Rita, the vision of successful marriage, Hollywood style.

Hawke lacks access to his subjects: Newman died in 2008, and Woodward has lived with Alzheimer’s disease for many years. But he finds a way forward. Throughout “The Last Movie Stars,” titled after writer Gore Vidal’s description of the Oscar winners, Hawke builds the case, first, that Newman and Woodward used art to probe their relationship. More movingly still, Hawke conveys the shared but unequal sacrifice both spouses made so that their long-standing partnership could be a greater entity than either could be on his or her own. The headline ends up making sense: The pair lived in public, but had unknowable inner perspectives that Hawke’s series only now brings to light.

Newman, who struggled with alcohol use, and who viewed himself and Woodward as “a couple of orphans” from their first meeting, used a planned memoir to come to a better understanding of himself; for reasons obscure perhaps even to him, he eventually burned the tapes, though some transcripts survive. Hawke, an outsider to the family, conscripts notable friends to narrate and comment on these transcripts, giving intimate insight into the stars’ thinking. Here, George Clooney plays Paul, with Laura Linney as Joanne.

There’s a shagginess that warms and distracts; the early-COVID vibes of Hawke convening pals on Zoom can feel as jarring as the images of young Newman and Woodward are nostalgic. But this hominess eventually fits two stars whose rural-Connecticut-based lives and images were rooted in performed authenticity. And Hawke’s volubility — at one point confessing to his daughter (and “Stranger Things” actor) Maya that he’s figuring out what the project is about as he makes it — is an intriguing match with a couple who recorded their most personal thoughts about each other.

Those thoughts can scorch: Linney, as Joanne, reflects upon spending Christmas Eve preparing presents alone, after her husband, known to the public as a devoted family man, has drunk himself insensate. Or they can be anguished, as we see in Clooney’s Paul after the death of son Scott Newman from substance abuse. Various Newman children offer loving but frank assessments of their parents, with a daughter of Newman’s abortive first marriage saying, “I can be disgusted with my dad when I think of my mom.” (Woodward tells us that all her children are loved, but that she might not make the choice to sacrifice her artistic self to parenthood if she could live life again — a chewily complicated thought.)

Yet what comes through clearest here is not rancor but a desire to think things through, a sense that marriage, fully realized, is a process of understanding oneself better through another’s eyes. That Newman and Woodward were often doing so on screen is a bonus. Hawke and editor Barry Poltermann cleverly marshal footage, with both partners’ work generously layered in. Newman drawing on personal demons in “The Verdict,” and Woodward her subsumption into marriage in “Mr. and Mrs. Bridge,” forged late-career triumphs out of sorrow.

Newman is a star for the ages, and the real pain we learn he felt and caused adds shading and dimension to our understanding of him. For many, though, Woodward will be hazier, and it’s her story that will break viewers’ hearts. Deep in the pair’s public life, Woodward accepts an acting award presented to her by her husband; the event has found a way to point the spotlight away from her even in her triumph. “It’s not all that easy being the husband of a famous motion picture star,” Newman quips as the crowd fawns; by inverting the expectation that Woodward is the plus-one of a star, the joke carries with it a real sting.

Hawke is a fascinating choice for this project: For one thing, his own movie-star marriage, to Uma Thurman, ended in divorce, lending wistfulness to observations about a particular sort of creative support. (He has remarried, and wife Ryan Hawke appears on camera and is credited as a producer.) Furthermore, Hawke’s image is that of the perennial student, earnestly devoted to honing his craft, in compelling contrast to Newman’s tossed-off charm.

This yields something special though: Hawke seems mystified by what it must have taken to make stardom, and marriage, look so easy, even as both partners paddled madly beneath the surface. This documentary series may not convince you its subjects were the last movie stars; their mastery of showing what they wanted the world to see feels utterly contemporary. But they’re unusually gifted ones — as, after spending six hours in their company, you’ll leave “The Last Movie Stars” wanting more.

All episodes of “The Last Movie Stars” will launch on HBO Max on Thursday, July 21.