Tommy Lee Jones, Meryl Streep — Robert Trachtenberg

At first glance, they would seem the unlikeliest of couples. The classically beautiful Meryl Streep was her New Jersey high school's homecoming queen and always compassionate and willing. Tommy Lee Jones, in contrast, came from rural Texas, where even in youth, his face seemed to mirror his hardscrabble environment, carved with lines like a peach pit. Equally harsh is his taciturn demeanor.

See also: Discuss your favorite Streep roles and costars

Strange bedfellows unless you ask director David Frankel (The Devil Wears Prada), who cast Streep and Jones as the leads in his film, Hope Springs, a portrait of a midlife couple grasping to regain their sexual passion. "Tommy's an extraordinary actor first, but he's also sexy," says Frankel. "It was important to have someone play opposite Meryl whom she found really sexy, so you could imagine a sexual history between them that had died."

In fact, Streep, 63, and Jones, 65, have more in common than it appears. Both possess sharp literary intellects. (During our photo shoot, Jones, a Harvard grad, cracks up when his wife offers a line about Southern literature from novelist Pat Conroy, and Streep, who got her M.F.A. from the Yale School of Drama, makes reference to the Roman poet Lucretius.) They claim four Oscars between them but cite their offspring as their proudest accomplishment. Married for 34 years to sculptor Don Gummer, Streep has four children, ages 21 to 32. Jones, wed to third wife Dawn since 2001, has a son, age 29, and daughter, 20, from his second marriage.

Now real-life empty nesters, Streep and Jones drew from experience for their roles in Hope Springs, in which 60-somethings Kay (Streep) and Arnold (Jones) sleep in separate bedrooms. That is until Kay decides to reignite the flame between them and drags her uninterested husband to an intensive marital-therapy week with Dr. Bernie Feld (played straight by Steve Carell). The film, with jaw-dropping directness in risqué sex scenes, follows Kay and Arnold as they attempt to reconnect. It was a daring undertaking for two mature actors, but Streep and Jones were undaunted. "The issues about sex are delicate yet universal," says Frankel. "Nobody thinks they're having enough sex — that goes for teenagers and people in their 70s. This movie is about intimacy, and Meryl and Tommy were excited to confront that. There was no squeamishness on their part."

There is, however, a bit of squeamishness on my part when I sit down with the actors to discuss sex after 60. To loosen things up, I offer them some wine. "No, thank you," Streep demurs.

"Sure!" bellows Jones, to which Streep responds coyly, "OK, then I'll have some, too." Wineglasses in hand, we begin.

Next: Streep and Jones on filming in the bedroom. »

Watch the trailer for Hope Springs, with Meryl Streep and Tommy Lee Jones.