Hello and thank you for allowing me to address your legal question.
Is your husband listed as an owner of the house on the deed? If so, then he can simply sign a quitclaim deed to convey his interest to you. But understand that doing so will not extinguish his rights in the house should you two get divorced. For purposes of divorce, a judge generally has the right to distribute marital property in an equitable manner without regard to title ownership.
If you owned the house prior to being married, then your interest up to the marriage may be considered your separate property. However, if marital funds were used to pay the mortgage, then your husband certainly has an interest in the property regardless of who is on the deed.
Having said all that, you may be able to create an agreement with regard to the house that will be enforceable after a divorce. It would be similar to a prenuptial agreement, except that it would be a postnuptial agreement. To create such an agreement that is enforceable in a divorce, you will both need to be represented independently by different attorneys (that would be the case for a prenup as well). Judges don’t like these kinds of agreements because of the likelihood of somebody inadvertently giving up his rights. Therefore, judges will not enforce the agreements unless it is clear that the person knew exactly what he was doing after being advised by legal counsel. Therefore, I suggest that you each contact different family law attorneys in your area to help if that is what you had in mind.
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DISCLAIMER: Please understand that the complexities of most legal problems cannot be sufficiently addressed in this setting. Accordingly, my post is intended as general information only, and should neither be construed as specific legal advice, nor as an adequate substitute for the retention of legal counsel.