What do you mean by "claim our house"? Do you mean claim an itemized deduction for real estate tax or mortgage interest? You can't both claim the same payments. The general rule is that whoever actually paid the tax or interest can claim it. If it was paid from joint funds you can split it up any way you like. And in the case of spouses who both own and live in the house, there is some leeway to allocate the payments any way you choose, as long as you both agree. But the total amount that the two of you claim can't be more than the total amount that you paid.
Also keep in mind that if you file as married filing separately and one of you claims itemized deductions, the other must also claim itemized deductions. You are not allowed to have one of you claim itemized deductions and the other claim the standard deduction.
