NY uses your entire AGI, which includes your husband's TN income, to calculate your tax on NY income. NY calculates what your New York tax would have been if you earned everything in NY, then prorates that tax based on how much of your income was earned in NY. The NY state tax interview will have a screen where you can allocate your husband's non-NY income.
Per the instructions for Form IT-203, page 5, How are residents and part-year residents taxed?, You will compute a base tax as if you were a full-year resident, then determine the percentage of your income that is subject to New York State tax and the amount of tax apportioned to New York State.
Additional source: ToddL
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