Can I refinance with husband on medicaid in nursing home.

No, you can't do this.  And from your question, I'm afraid that you may have committed Medicaid fraud, and you need to see a lawyer about this, as soon as possible.

Medicaid has a "means test," to get nursing home care under Medicaid a person has to have a very low net worth, usually no more than a very few thousand dollars.  You did the quitclaim deed to get your husband under the limit.  Unfortunately, what you didn't know, and probably didn't understand in the paperwork, is that there is a "look-back" period of three years, where any transfers for less than fair market value get added back into the person's net worth.  Your quitclaim deed was the kind of transfer that gets added back.

This will come out, sooner or later, and you'll be expected to come up with the benefits paid, and you may well have no choice but to sell your home.  You need a lawyer for damage control, right now.