The key, he added, is variety: the sincere parts need to be taken seriously, and the funny parts need to be funny. “I think the mistake most directors make is to attempt to play one thing in the production,” he said. “It doesn’t work.”

This year marks the 200th anniversary of Offenbach’s birth, a landmark which has passed without much fanfare in the United States, where he is probably best known as the composer of “Les Contes d’Hoffmann,” his only full-fledged opera. But in Europe, productions have proliferated. In an interview, the American musicologist Jacek Blaszkiewicz called Offenbach “the prototypical European satirist. I think European audiences still, to an extent, kind of get the joke.”

For 20th-century theorists like Theodor Adorno and Siegfried Kracauer, Offenbach was a political figure; they claimed his satire deconstructed the decadence of Second Empire Parisian society and unmasked hypocrisy. More recent writers have taken a milder tack, casting Offenbach as an entertainer with satirical tendencies.

“This is not like a didactic political-polemic theater here,” Mr. Kosky said. “This is half-naked dances. There were political strands in it, but he was above all the entertainer, you know; he was writing music that was influenced by vaudeville and variety.”

Massively popular, Offenbach was both a Second Empire insider and not: a German Jew living in Paris, but one who had acclimated to local culture and whose works allowed the social elite to gently laugh at themselves. In “Orpheus,” he allowed the assembled society to see themselves as the work’s gods and goddesses — but those deities spend the evening lying, cheating, whining and otherwise misbehaving.