My mom likes my band's music, as well as some stuff from the 60s, 70s, and 80s. Primarily AOR types of stuff. But, she's more into individual songs than bands. You should see her eyes light up if you talk about Thriller.
My dad is a bit more open-minded, although he tends to like more traditional forms of music- old country (Johnny Cash, Hank Williams), classic rock, classic pop, jazz, that sort of thing. I played Acid Mothers Temple for him once and all he could say is that it was "different". His primary complaint with a lot of "modern" music is that it doesn't "take off"; but by that he really means it doesn't follow the blues-derived I-III-IV structure prevalent in mid-20th century pop/rock.
I can agree with both of them of some stuff (the Beatles, Johnny Cash, the Temptations) better than others (Starship, Hank Williams)...