Birth control and insurance question?

I'm 21 years old, I don't have a boyfriend, but I do have a 'friends with benefits' who shows his face every now and then. I always use condoms to prevent std's and unwanted pregnancy, however, I've been thinking I want to add the pill to add an extra layer of protection. My question is, if I go into Planned Parenthood, will it show up on my insurance? I'm still on my parent's plan, and normally this would be fine but I already tried to talk to them about this a while back and they weren't pleased. I would love for my parents to understand but they're a bit old fashioned and have the idea that you shouldn't be having sex if you're not in a relationship with someone. I just want to take every precaution I can, because I'd like to be a little older when I have kids. Thoughts?