The key is the mortgae

First, you two need  confirm the equity on this house, and have an agreement who will keep this house  in your deviorce

Normally, the party keeping the house will have sole responsibility to pay the mortgage, but anorther part should have the right to forclosure the hosue if the mrotgage is in default.

all of these should be in the final aggreement.

However, bank will still think the mortgae under your both name.  still have the credit score risk, except the loan is refinanced or paid off by case.