He now knows that we can both remain on the current loan after our D and as part of the settlement it can be stated that he no longer has any financial or other liability with respect to the house. Also, he does not want any equity out of the house. He said he will sign everything over to me.
Really? It's my understanding that, although he may sign the title over to you, if his name is still on the loan, the mortgage company will still hold him liable for the payments if you don't make them - regardless of what the divorce decree says. So - it's really foolish for a guy in a divorce to sign over the house if it hasn't been refinanced in your name only.
If he's really pushing for the refi, I suspect either he's trying to do the right thing, but wants to reduce the payments so there is less chance of you defaulting on the loan - OR he's gonna push to get his name off the new mortgage.
Are you planning on staying in the house? Can you afford the payments on your own? If not, I wouldn't refi it. Get some financial advice.