If you listen to an average top rock chart radio station, they’ll play a mix of both.
You could also go with music closer to the middle of both of the genres, like
Evans Blue
Linkin Park
Breaking Benjamin
Audioslave
Shinedown
Switchfoot
Finger Eleven
Lots of other stuff, I’d really just play a mix..

It’s not really bad for your relationship, imagine if he was into hardcore rap and techno, and you loved jazz, or country…