They can still file separately ("Married, Filing Separately") - owning a house together does not affect their filing status options.
One of the main requirements for "Married, Filing Separately" is that both spouses must use the same method for calculating deductions - standard or itemized.
If they choose to itemize deductions, they can allocate the deductible mortgage interest and property taxes in any way they wish.
@xmasbaby (above) provides excellent additional detail on the limitations, advantages and disadvantages of "Married, Filing Separately"
