I don't agree that his response to the news of the debt is understandable or reasonable. OK, I can see how it would be a shock, but what he has done is not mature or in any way helpful either from the pov of the relationship or the problem of the debt. There are plenty of people who post on Relationships who have experienced all kinds of betrayal and they post from their homes, where they somehow manage to deal with children, babies, illness as well as their feelings. This man has gone off to sulk because he thinks his relationship can afford the luxury of his immaturity.
To flatly state that they must sell the house in order to instantly retire the debt is just silly, and to refuse to discuss anything yet to demand sex (taking the OP at face value here) is not on.
OTOH, OP, I do think you need to find out exactly where your family finances stand and see what steps you can take, see if you can present this twat with a plan of some sort, or evidence that you have contacted the creditor and that the debt repayment is not urgent. If he insists on his way or the highway, then you have to see where you will take the relationship from there.
You should also go to a solicitor and talk about your rights, if any, to the family home.
Sometimes, if you want someone to talk reasonably and they are sulking, it helps to ignore them for a while, and they come back to see what is distracting your attention. It used to work that way when the DCs sulked anyhow...