You have no right to "add" your name to a quit claim deed. It is your husband's decision as to whether to add you to title or not. If he chooses to add you, he can do so by drafting (or going to an attorney to have drafted) a Quit Claim Deed.
You do have two rights in the property right now if you are residing in the house as your marital residence: (1) you have "homestead" rights which precede any other creditor's rights to be paid from the property; and (2) in the event of his death, were there to be any equity in the property, you have the right to 1/3 of his estate under probate law. Luckily, though, you do not have any obligations under the mortgage, since you would not have signed the loan documentation, so to the extent that the property is foreclosed on, you will not owe any money.
This answer does not constitute legal advice and does not and is not intended to create an attorney-client relationship. The law may vary depending on the state in which you reside. It is intended only to give some direction in which to seek assistance.