homestead exemption & taxes for unmarried co-owners

My long time partner, and I just bought our second house together. I never applied for a homestead exemption on our old townhouse (which we sold about a month ago) but I am going to do it for our new house.

We own our new house 50-50, but I am worried about not being able to get the full exemption if I apply for homestead exemption as both being 50-50 owners. I usually file as head of household w a standard deduction, (because we have two children together), and he as a single filer with itemized deductions (property taxes, medical bills, donations, etc).

What should we do here? Having a hard time finding information about how we can get the full exemption value as an unmarried couple Filing separately. Should he filed a homestead exemption as being the 100% owner? Or should we do 50-50 and can he cab claim the full exemption?

Thanks!