There are laws in place to protect you and ensure that you will not have to move out of the house. If he files for divorce and was the one to move out of the home, leaving you there he is acknowledging that you have a right to be there.
The rules for this vary by state. In most states, however, anything that was bought during the marriage is the property of both spouses. This would include if mortgage payments were made during the marriage. If, however, he owned the house before you got married, it is his alone.
Depending on what state you live in, the wife/spouse is able to get 50% of whatever property/belongings you have had through the time of your marriage. Even if your name is not on the Deed. Check with an attorney to see if your state applies