Does adding your spouse to your medical coverage cost more?

My wife and I are newlyweds, and we both had medical coverage with Blue Cross Anthem. I recently became eligible for benefits at my job, but with the prices they are offering I don't see where the benefit is. So I've decided to go with someone else like Kaiser if not stay with Anthem. I figured having medical coverage under the same plan should be cheaper, but I'm not sure. Yes I know, talk to a representative. I'm trying to, it's just Anthem's customer support structure is so stupid, I have to email them and wait for a call back. It's been 2 days already and still no reply, which is why I'm asking for your help. thanks.