Divorce is a different answer than dies first. Dies first could have a lot to do with his will... Divorce is (absent prenuptial agreement) governed by case law and statute.
So, for the divorce the answer would be (normally) that he would get the house although you would be entitled to payment for an equitable share (usually half) of the INCREASE in value from 4 years ago. If the house has decreased in value, you will not likely be entitled to any share of the house. In a divorce, this situation would require an appraisal as of the date of marriage and as at the date of divorce in order to determine the increase. As a practical matter, it sounds like his name is on the debt, so at least you are not tied to the debt on the house. BTW - I would be reluctant to allow him to refinance it during the marriage without reaching some kind of an agreement as to how to handle the debt... If he jointly titles the property in both of your names, you would likely get the house upon his death and in a divorce, you would have a stronger interest in the entire value of the property (rather than just the increase in value). Hope this helps.