Driver does pick the music (I tend to agree with Dean), however Driver is also aware Passenger dislikes particular band/genre, Driver does not go out of his/her way to play that band/genre.
For instances, my musical tastes are wide and varied. And I happen to like country music. My best friend hates country music (she says, except for when she does like it because she's wishy washy like that), so when she's in the car with me I don't go out of my way to play country music. However, if I throw on one of my mixes and it has country on it, I'm not dive bombing to get it off either. But I will generally pick more of my rock varieties with her since I know she likes it and I like it.
I had one person who insisted we had to listen to his music! We were carpooling for work and one day I came to pick him up with Kid Rock on. He told me to wait a second, ran inside his house and came back out, as I was driving he pulled out my CD and put his metal one and said "That was just too hillbilly! Got us some good music", I popped his CD out and put on a classical music station and told him if he touched the radio he was walking to work.