Leaving aside the factual problem of him not qualifying: he should also run the numbers in the context of the bigger picture. Does it really save him much money? The refinancing costs, especially for a significantly lower rate, in relation to the new interest rate will make it a fairly long time before he will actually save money. While this obviously depends on the difference between the new rate and the current 5.5% as well as how much longer he will actually still own the property it is still something to consider.
Another idea: why not sell the place to, for instance, you, during which time you could refinance in your own name and have him rent the place from you, making you a landlord with all the benefits of deducting interest etc.? You would have to crunch the numbers. Again. Also: maybe even (partial) owner financing for the downpayment part that you would have to come up with could work? All this is, of course, dependent on you being able to qualify for a mortgage to begin with. ;-)
@Taye N. With that amount of income, no way he will qualify for a new mortgage. As @Russell Brazil suggested your only hope is a FHA streamline refi, where you can get a lower rate, but no cash-out. If the current loan is not FHA then you might be out of luck.
Anyone else with more income that can be added to the mortgage?
Leaving aside the factual problem of him not qualifying: he should also run the numbers in the context of the bigger picture. Does it really save him much money? The refinancing costs, especially for a significantly lower rate, in relation to the new interest rate will make it a fairly long time before he will actually save money. While this obviously depends on the difference between the new rate and the current 5.5% as well as how much longer he will actually still own the property it is still something to consider.
Another idea: why not sell the place to, for instance, you, during which time you could refinance in your own name and have him rent the place from you, making you a landlord with all the benefits of deducting interest etc.? You would have to crunch the numbers. Again. Also: maybe even (partial) owner financing for the downpayment part that you would have to come up with could work? All this is, of course, dependent on you being able to qualify for a mortgage to begin with. ;-)