I have a roommate who has people over for parties all the time and doesn't respect other roommates privacy. I own the furniture in the house and all the bills are in my name. He pays one third of the rent, I pay the bills and he is on the lease. Do I have any rights to ask him to leave?

You certainly can "ask" him to leave. But, if he is signed on the lease then he is an equal tenant along with you. Therefore, he can refuse to leave and there is little you can do about it. Only the landlord can file for eviction and you are not his landlord.