I am so sorry for you situation.  What you really need here is a good lawyer to help with this matter.  Technically the fact that he has committed adultery is not a factor in the distribution of the house or the debt.  Court's don't consider it (unless in some instances where the debt was accumulated to pay for adulterous behaviour).  Generally marital property is property acquired during the marriage and how it is titled or who has been paying the mortgage does not come in to play.  Your income during a marriage is considered marital income.  You need help from someone to sort through things.  Bring all the documentation that you have.  Good luck to you.