Why should you sell just because he wants to come off the mortgage? He can't come off it. So your other option (apart from selling) is to tell him that & go on as you are, so long as you're able to cope financially. He could conceivably go to Court to try & get an order for sale but, given the facts you set out, I wouldn't like to bet on the likelihood of a judge giving him one. He has no financial interest in the property (all the equity is yours) & is not having to pay anything towards the mortgage.
There is no point doing an IVA - among other things, you would be expected to re-mortgage in year 4 to raise money for the creditors out of the equity. If you really can't go on as you are, far better in my view to bite the bullet, sell & settle the debts. You would need to keep back some of the equity for the inevitable expenses of moving, rent deposit & rent in advance etc. etc. so you might not have enough to pay off the debts in full. However, given the circumstances it should be possible to get creditors to accept a full & final settlement offer. Stepchange should be able to advise you on this.
Are all the unsecured debts in your sole name? If any are in joint names or his sole name then he has a responsibility for them.