For most states of which I assume Ohio is one that does this, if you are a resident of that state then all income from all sources regardless of where you earned it, is taxable by that state of declared residence. Now while your federal taxes allow a credit for foreign taxes paid, I'm assuming that Ohil does not allow for that type of credit on your state taxes.
In the future, I can only suggest you always file joint for both federal and state, because in my experience for a married couple to file separate will always cost you both more, tax-wise. When a married couple files separate then they both automatically disqualify themselves for a number of deductions and credits they would otherwise qualify for if filing joint.

  It only appears that Ohio is taxing all your income.

Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT)   does this by allocating your income as either Ohio or non-Ohio. W-2 income will be allocated by the state name abbreviation shown in box 15 of your W-2. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income.  

This system allows Ohio to apply their highest tax rate, based on your total income, while only taxing your Ohio income.

Ohio has a nonresident credit allocation form. IT NRC             http://www.tax.ohio.gov/portals/0/forms/ohio_individual/individual/2017/PIT_ITNRC.pdf