Marriage Certificate Question

DH and I got a document from the church where we were married. Is this the only thing that is going to come? We got married three weeks ago and I was assuming I would get something from the state. The document we have said something about complying with the laws of NYS. I am wondering if this is the only thing we are going to get because I want to put my husband on my insurance as soon as possible, as DH has not had a physical since the first George Bush was president!

Thanks in advance.