Will one of them be keeping the house? If so, they'll need to get a valuation done to determine market value and generally the other person is paid half of the increase since purchase price (depends on the splitting of other assets) The title will need to be transferred into 1 name (requires some legal work) and the mortgage refinanced. This can sometimes be difficult because the mortgage is usually taken out with 2 wages and is not able to be supported by 1 person. I used to work in mortgage lending and whatever he does - don't get advice from the bank lender, they only have their sales target to worry about. If the situation is complicated i would advise him to seek legal advice.
HTH