There is one type of “Jewish music” that is neither “Jewish” nor “music”: that junk that assaults one’s ears in New York-area supermarkets. The “music” (as distinguished from the lyrics) is Israeli pop music which sounds like generic pop music of the US and Western Europe and is awful and has nothing Jewish about it. The lyrics – I only know the English lyrics – are too simple-minded to be Jewish, and the singers have absolutely no training other than listening to other singers of the same junk.
A lot of jazz and other music is themed around romance that is not connected with marriage, and I do not see how it can be considered acceptable listening for frum Jews.