Under Texas law your homestead is an exempt asset and is not a countable asset when you run the calculations to qualify for long term care under Medicaid. Generally speaking, Texas law allows you to sell your homestead property and reinvest the proceeds from the sale into a new homestead within 6 months. During that 6 months, the proceeds from the sale of your first home maintain a homestead-like status. I haven't researched this rule as it pertains to Medicaid recently and so I advise you to seek the advise of a Texas Elder Law Attorney before taking any steps to sell your current home.
This post is meant for educational purposes only and does not create an attorney-client relationship between us.
You have two separate questions or issues combined in one. If the house is in both names, your husband, or his agent or legal guardian if declared incapacitated, must be able and willing to sign the deed selling your home. That is often the easy part, but may require you to take legal steps to secure that consent. I do not know, and I am not authorized to give legal advise regarding the laws of Texas. There may be a marital right that needs to be extinguished by securing his consent if the house is in joint names, OR, simply because it was a marital residence.
The other question concerns elder law and Medicaid. As a community spouse you should be able to reside in a residence without it being a "countable asset" for Medicaid purposes, but each state has different rules. A very old recommendation, which may or may not still be valid, although emotionally upsetting, is to divorce your husband and thereby eliminate any need for you to support him.
This certainly requires consultation with a Texas Elder Law Attorney. The National Academy of Elder Law Attorneys can refer you to one, as can your Texas State Bar Association.
Medicaid questions are most generally tied to state law and must be answered in the context of how each state interprets and implements their Medicaid enacting law. That said, I don't know Texas law, but in Kansas, you should be able to sell the house and invest the proceeds within a reasonable time in a different house. In Kansas the house is an exempt asset and you should be able to switch houses without trouble. In the event that your Medicaid administrative agency (SRS in Kansas) has issues with the conversion into cash for a short time period, you could do a like-kind-exchange (Section 1031 exchange for tax purposes) and escrow the proceeds with a qualified intermediary to facilitate the house swap. That way you never come into possession of the cash between houses. This should work. Good luck. I would recommend that you talk to your state Medicaid agency about this issue and they should be able to guide you through the process. I find the agency folks really helpful in most cases.