I might even be using it wrong in the example. How are these statements usually structured, and what's the implication of using this construct ("he is a happy, if quiet, boy") rather than something more straightforward? The examples I can think of usually seem to have a adjective in the parenthetical that is somewhat counter to the main statement.
Can it be a verb instead of an adjective ("he is a quiet, if amused, boy")?
Sorry if this has been answered, it's a very difficult thing to search for without knowing the name for it (if there is one).