Elise (Veerle Baetens) and Didier (Johan Heldenbergh) make beautiful bluegrass music for a European audience in “The Broken Circle Breakdown.” (Tribeca Film)

Bluegrass musicians Didier (Johan Heldenbergh) and Elise (Veerle Baetens) harmonize magnificently onstage and off in “The Broken Circle Breakdown.” They have the kind of ardent relationship that might make other couples jealous. But the Flemish drama doesn’t deal just with the fortunes of love at first sight; it examines in aching detail the limitations of a seemingly perfect relationship when tragedy strikes.

The movie, based on a play by Heldenbergh and Mieke Dobbels, bounces around in time and opens on a painful note. Didier and Elise are at a hospital in Ghent, Belgium, with their young daughter, Maybelle (Nell Cattrysse), who is undergoing treatment for cancer. While each parent is taking the news in his or her own way, they vow to put up an optimistic front around Maybelle.

From this grim opening, the movie jumps back seven years to the couple’s early relationship and the thrill of getting to know each other. Elise, a tattoo artist, gives Didier a tour of her copious ink, while he teaches her about the roots of Appalachian music. Didier explains that to combat the misery of an impoverished existence in the mountains, musicians sang songs. And that, too, is what director Felix Van Groeningen accomplishes, peppering the film with musical interludes of the couple performing onstage with their band.

Some moments of the movie might leave viewers feeling bereft or gut-punched, but the sublime sounds (along with the sweet and silly scenes of the pair falling in love) provide respites from the sorrow. You could call the movie a musical, though more in the small-scale sense of “Once” than “Les Miserables.”

Late in the film, the plot takes a strange turn, pitting science vs. religion with an argument that seems invented to create tension between the film’s protagonists. But up until that point, every moment feels both real and necessary. Even small details provide important insights, from Elise’s tendency to tattoo over the names of former loves to Didier’s sometimes aggressive ways of explaining his personal philosophies.

In adapting the play for the screen, Van Groeningen chose to tell the story out of order, and it works. Seeing portions of an outcome before we know why — say, Elise unconscious in an ambulance — fuels a mysteriousness that keeps the viewer watching. Although the stunning cinematography alone might be enough to do that.

While film editing is often an unsung profession, Nico Leunen deserves special praise for bridging the temporal divide of various vignettes, sometimes in exceptionally clever ways. When Maybelle, face-painted to look like a tiger, unleashes a roar, it melds with the low growl of the couple’s truck as the movie cuts to a scene from the past.

With its exquisite depictions of suffering, “The Broken Circle Breakdown” is not always easy to watch. But, as in life, sometimes there’s beauty to be found in the pain.

★ ★ ★

Unrated. At Landmark’s E Street Cinema. Contains strong language, nudity, sex and mature themes. In Flemish and English with subtitles. 111 minutes.