Unfortunately, there is likely not much to be done that can help for reducing your tax due when married filing separately.
As you may know, when one spouse files separately using itemized deductions teh other spouse must also use itemized deductions even when their total of itemized deductoins is less than the standard deduction.
He is technically correct that mortgage interest can not be claimed for a person that is not liable for the loan. You may want to check with the mortgage company to confirm that is correct. Most mortgages for jointly owned property are in both names.
If you both claim the same payment twice then both returns could be examined. So, you will have to file based on what you can agree to splitting the amounts that were paid from joint accounts. This will apply for taxes, charitable contributions, etc.
Although not of any immediate help, you can ask your attorney to consider including your contributions to his loan, that he deducted, when splitting marital property. That is, if he insists it is only his loan then perhaps you have a claim that he should reimburse you for what you paid toward his loan. That idea might even presuade him to let you split some of the other deductions. Or, he takes the interest and you take the taxes and charity (for example).
I hope this helps to know interest on a loan is only deductible by the liable person; even though it is likely not what you wanted to hear.
Yes, it is possible for a refinance to be only in one name; but as I said it is not the usual manner in which it is done.
For you to be on the loan you would have had to sign the loan application or other documents. If you did not sign anything then you would not be on the loan.
I hope this helps; but whether or not you are on the loan you and he will have to split the amounts or risk having both returns examined for not matching the total that is reported the IRS.