If my husband and I bought a house 6 years ago bit it is only in my name because of my husbands credit, what happens to the house if I die?

Based on your question, I assume that you do not have a Will.  It is important for you, as well as for anyone who owns assets, to have a Will.  If you die without a Will, the laws of your state will govern how the assets that you owned at your death are distributed.  These laws are complicated, and chances are they will not result in the distribution of your estate in the exact way that you would like it to be distributed.  For example, under Connecticut law, if the decedent had no Will, depending on whether a person is survived by children or one or both parents, the surviving spouse may not receive all of the deceased spouse's estate.  In certain of these situations, in the absence of a Will, a specified portion of the estate will go to the surviving children or surviving parents, and the remainder will go to the surviving spouse.  All of this can certainly create problems if you die without a Will.  In order to ensure that your assets are distributed the way you want them to be, you should definitely get the advice of a lawyer regarding inheritance issues, and do a Will.  The same applies to your husband, even though his name is not on title to your house.  He should have a Will in order to direct how he wants his assets to pass upon his death.  That will avoid the situation where his estate could be distributed according to the types of laws that I described above instead of according to his wishes.