The house or residence (including a condominuium or coop apartment) is an exempt asset not subject to the claims of the nursing home as long as your mother remains alive and is living in the house or, if she is ill and has to go to a hospital, etc. still intends to return to the residence.
Your mother under Medicaid laws, which are federal laws administered separately by each state, is called the "community spouse" -- this means she is living in the couple's home in their community. The husband is called the "institutional spouse" because he is living in an institutional setting -- a nursing home or long term care facility. In most states your mother can retain about $100,000.00 and the residence she is residing in as exempt assets. Sometimes other assets such as IRA's may be exempted if certain rules or payment schedules are complied with by the community spouse.
The real risk exists if your mother dies first -- before your father: in that situation, if their assets are held as joint assets (with right of survivorship), all of those assets will go to the spouse who lives longer. Then, there is no community spouse exemption and the state and the nursing home can apply a lien to those assets which are now owned by the "institutional spouse"--this means the nursing home can take those assets for your father's care.
There are legal ways to avoid this "medicaid trap". I strongly recommend that you consult with an elder law attorney in the immediate future to identify and execute appropriate planning strategies.
Generally, I agree with the first answer, but the community spouse limits on assets in South Carolina are somewhat more restrictive than the $100,000.00 the previous answer cites. I would strongly suggest that you seek the counsel of an elder law attorney as soon as possible. The SC state bar has an elder law committee made up of members who practice in the field of elder law. Also, the National Academy of Elder Law Attorneys has a SC chapter. NAELA's website is www.naela.org. They can refer you to a competent elder law attorney in your area.
NOTE: nothing in the above answer constitutes legal advice or creates any attorney client relationship or representation. Any representation or relationship with the responding attorney would be evidenced by a written fee agreement outlining the nature and scope of representation and supported by payment of a fee as consideration for the attorney's services. The above answer is submitted for purely educational purposes.