Debts created during the marriage are the responsibility of both spouses. Walking out has nothing to do with who is responsible. In the course of the divorce the two of you will have to allocate assets and debts equally. In the course of that process the person who gets to keep the house is most likely going to have to take the debt. Otherwise there would have to be a significant offsetting payment to equalize things, and hardly anyone can afford that. In fact if you can afford the offset, you may as well just pay off the debt. Once the debt is allocated, there is almost always also an order that joint accounts be closed. This will mean the real property debt will have to be refinanced. In current lending conditions, that doesnt' always have to be immediate; courts understand the economy, but it will have to be done eventually so that the other party is no longer liable.
