A type of musical we don't see very much any more is what I (and others on rec.arts.theatre.musicals) used to call the "serious musical comedy," which is to say a serious, basically non-comic story told in the style of a musical comedy. Examples I can think of include FIDDLER ON THE ROOF, FOLLIES, GYPSY, CABARET, I CAN GET IT FOR YOU WHOLESALE, A TREE GROWS IN BROOKLYN, and my favorite of them all, FIORELLO!
None of the above shows can be described as "musical comedy" (and none of them billed themselves as such), yet they're not really "musical plays" of the SHOW BOAT or CAROUSEL kind, either; they don't fuse the languages of musical comedy and operetta the way SHOW BOAT did. A show like FIORELLO! or GYPSY is a punchy, fast-paced piece, with hardly a trace of operetta in it; it uses the theatrical and musical language of musical comedy even though it's not a comedy.
This style of musical never seems to have really taken off -- shows like FIORELLO! are exceptions to the general rule that the
musical-comedy style is mostly used for comic stories -- but I love it. FIORELLO! is a wonderful example because even though it deals with politics, death, war, and corruption, writer-director George Abbott conveyed the serious themes in the style of a comedy -- the book (which I still consider one of the very best books ever written for a musical) isn't necessarily ha-ha funny, but it has the feel of a comedy. So does the score by Bock and Harnick, which goes for the musical-comedy aspect of strikes ("Unfair"), political corruption ("Little Tin Box") and unrequited love ("Marie's Law") One of the great examples of the "Abbott touch" is that he threw out a rueful ballad originally intended for Marie, and got Bock and Harnick to convey the situation through comedy instead, by writing "Marie's Law," where she obliquely and comically sings out her frustration at loving a man who doesn't love her back. ("My law will state, to whom it may concern / When a lady loves a gentleman, he must love her in return.") And it does all this without trivializing these things; indeed the musical-comedy style makes the themes seem more direct and honest than, say, a deadly-serious, mournful musical scene about corruption in New York politics.
Another great serious musical comedy by Bock and Harnick is FIDDLER ON THE ROOF, which is the same thing: a serious story, yet funny all the way through and using the arsenal of musical comedy (in particular, the oldest, corniest, most effective Borscht-belt jokes, right down to the "You're right/you're right/you're also right" routine) to tell a serious story. Nowadays, FIDDLER would probably be written and staged as a gloomy tragedy about poverty and violence; indeed, we keep getting revivals of FIDDLER that think they're being daring by taking out the Borscht-belt comedy (as the movie did to a large extent) or playing up the gloomy aspects of the story (as the recent revival apparently did). They don't understand, as Jerome Robbins did, that just as a song can be more effective if it expresses emotion obliquely -- don't say "I love you," say "They all laughed at Christopher Columbus" -- a whole show can be more interesting if it plays like a comedy, which lets the big serious moments (the pogrom in FIDDLER, "Tomorrow Belongs to Me" in CABARET) pack more of a punch by contrast with everything that surrounds them. And because musical comedy is by its nature less sentimental than the musical that's serious all the way through (a song that mocks love is "tougher" than a straightforward torch song), serious musical comedies don't have the mushiness that Rodgers and Hammerstein musicals sometimes (not always, but sometimes) display.
In the years since the original CABARET, I can't think of many shows that have used the serious musical comedy style. ASSASSINS is close, but with its big long musical scenes and big Message Moments it doesn't really have what I'd call a musical-comedy score. Now that musical-comedy methods of songwriting and storytelling are "in" again, I wouldn't mind seeing some new attempts to tell a serious story in a musical-comedy kind of way; it would certainly be an interesting alternative to the inflated, self-important "serious" musicals we often get. At its best the serious musical comedy can deal with subjects off-limits to pure comedy, while preserving a hard edge that the musical play often loses.