My dad wasn't much of a music person. He'd occasionally listen to classic rock radio while driving, but also didn't mind driving in silence.
My mom listens to a mix of classic and semi-modern rock, but nothing very heavy. My record collection began with some of the remains of my moms old collection of mostly classic rock. No real heavy hitters, but some good stuff in the mix. She was definitely the bigger influence on my musical journey.
Everything else I've pretty much discovered on my own. My parents were usually cool with me listening to whatever I wanted, even if they personally didn't care for it. Along the way, I've introduced my mom to newer bands that she can appreciate as well.
"It's good to be the king."