Kurt Weill and Lotte Lenya married, divorced, remarried, and appeared headed for a re-divorce right before Weill’s death at the age of 50. The two frequently lived hundreds of miles apart. Weill had a mistress for six years; one of Lenya’s many lovers took advantage of the chaos in 1930s Germany (Weill, a Jew, had already fled) and ran off with her money. Early on, when she complained to Weill that she felt ignored, he answered, “You know you come right after my music!”

Depending on their taste for perversity, anybody looking to turn this unlikely love story into a Broadway musical is either sitting on a gold mine or destined for trouble. Or perhaps both, as is the case with “LoveMusik,” the ambitious but schizophrenic effort by director Harold Prince (who directed Lenya in 1966’s “Cabaret”) and book writer Alfred Uhry. Using some two dozen of the composer’s haunting songs and eliciting superb performances from Michael Cerveris and Donna Murphy, “LoveMusik” comes tantalizingly close to explaining how the son of a cantor and a former child prostitute formed one of the 20th century’s most curious romances. Ironically, though, the project is foiled by the very thing that made it so tempting in the first place — Weill’s own versatility.

On a professional level, the symbiotic nature of their collaboration proved complicated: Lenya found great acclaim in Europe singing Weill’s music in the 1920s and ’30s, but her difficulty at adapting to a more “American” sound led to virtual obscurity during her first two decades in America. This did no favors to their already tempestuous relationship, especially juxtaposed with Weill’s relative comfort in acclimating himself. While nobody would confuse “The Threepenny Opera” with later works such as “One Touch of Venus,” Weill’s brand of woozy astringency remained fairly consistent even when he parted ways (bitterly) with Bertolt Brecht and adapted to Broadway’s glossier demands.

The Brecht collaborations have so overshadowed Weill’s career that it’s easy to forget just how many other collaborators he had. Any discography that includes lyrics by Oscar Hammerstein II, a 29-year-old Alan Jay Lerner, and Ira Gershwin stands out even without including Brecht. Now toss in Ogden Nash and Howard Dietz. Oh, and don’t forget his “Street Scene” lyricist, Langston Hughes.

This embarrassment of lyrical riches stymies Messrs. Prince and Uhry, who are left with a stylistic smorgasbord that continuously wriggles free of any unified tone and leaves the complexities of the Weill-Lenya relationship unexplored. (Any cohesion in the “LoveMusik” score comes primarily from Jonathan Tunick’s superb — and mercifully synthesizer-free — orchestrations.) Too many selections are less notable for furthering the narrative than they are for representing each major Weill work. While “LoveMusik” is technically a jukebox musical, this sort of inclusion-by-obligation makes it feel more like a checklist musical.

Hammerstein and Dietz are checked off via two frivolous tunes from the World War II-era “Lunchtime Follies,” an anti-Hitler ditty called “Schickelgruber” and a paean to the working man called “Buddy on the Night Shift.” And while neither adds much to the narrative, the worst offender is “The Illusion Wedding Show,” a vaudevillian number from “Love Life” that has been shoehorned into Act II to convey a message — marriages can be complicated — that had been spelled out more than two hours earlier. The soloist on this song, John Scherer, is largely wasted in the role of George Davis, a homosexual producer who would become Lenya’s second husband (third if you count both marriages to Weill).

David Pittu fares somewhat better as Brecht, depicted here as a hypocrite and a bully, stewing in a trailer with a trio of harpies and whining about money he’s owed. Although the Weill-Brecht partnership is also addressed only cursorily, with no real explanation given for their acrimonious split, Messrs. Pittu and Cerveris give a plausible account of the team’s shifting fortunes and lingering resentments.

The performances by Ms. Murphy and Mr. Cerveris, meanwhile, are nothing short of dazzling; their Lenya and Weill join Frank Langella’s Richard Nixon and Christine Ebersole’s “Little Edie” Beale as the rare stage impersonations that do honor to the actual person, to the text, and to the audience all at once. Ms. Murphy, who has squeezed her formidable singing voice into Lenya’s chiming honk, exhibits her character’s self-protective swagger as well as her vulnerability. And Mr. Cerveris, employing a higher vocal register than usual, gives vivifying energy to this complicated man. He touchingly depicts a Weill who finds refuge in his music, palpably shedding his discomfort when he begins to sing or play the piano, and is as baffled by his deep affection for Lenya as she seems to be.

For every awkward interpolation in “LoveMusik,” Mr. Prince offers at least one ingenious rethinking from the Weill catalog. Take “That’s Him,” a soufflé-light collaboration with Nash:

You know the way you feel when you smell bread baking
The way you feel when suddenly a tooth stops aching
Wonderful world! Wonderful you!
That’s him.

Originally sung by a smitten woman, the song here becomes a poignant ballad as the oft-cuckolded Weill speculates about the joy a new paramour inspires — “the way you feel that you really shouldn’t feel” — in his beloved Lenya. Sung exquisitely by Mr. Cerveris, “That’s Him” changes in Mr. Prince’s hands from a song of adoration to one of anguish.

That staging, along with a gorgeous opening duet of “Speak Low,” benefits from the fact that Ogden Nash wrote insightfully about unconventional pairings. (Both songs come from the boy-meets-statue romance “One Touch of Venus.”) This quality is stubbornly absent for too much of “LoveMusik.” Compellingly sung and indelibly acted though it may be, it is frequently forced into an awkward choice between highlighting the love or the musik. The love too often comes in second – a fate that only Weill might have appreciated.

Until June 17 (261 W. 47th St., between Broadway and Eighth Avenue, 212-239-6200).