The fact that he lives in a nursing home does not really change anything about your filing status. You still file jointly as though you lived together because absences for medial treatment are considered temporary.. The only difference is you may have a large medical expense deduction. If his presence at the nursing home is due to the need for medical treatment, you can deduct the full cost of the nursing home. If he is there partly for medical treatment and the rest for personal care, then you can deduct the portion of costs for the medical treatment.
Of course, medical expenses are only deductible for the portion in excess of 7.5% of your Adjusted Gross Income and only then if the total of all itemized deductions exceeds your standard deduction.