What happens if neither spouse can afford the house after divorce?

Just found out my wife has been cheating on me, and I'll be getting a divorce. Here's the situation: We just refinanced our home in November and have virtually no equity in it. Since the housing market has turned, it's unlikely that we'd get what it appraised for in a sale. So what are my options? If we both stop paying the two mortgages, it will go into foreclosure, but I'm unclear what would happen after that. Could someone please explain?