Get your taxes done using TurboTax

First, do your federal data entry, then your NY data entry, then your NJ data entry last. The rule is to do the non-resident state(s), then the resident. You will be filing jointly federal and states.

Then, when you go through the NJ interview, if you are using the TurboTax online product, you will see the following helpful screen:

This addresses your issue: you will (both) report your income to New York, get taxed on it, BUT the New York taxes (City, too) will carry to the NJ return as a "credit for taxes paid to other jurisdictions". In other words, the taxes on your spouse's NJ income will go to reduce the NJ taxes for both of you.

Later, in the NJ interview, you will see a screen called "Summary of Taxes Paid to Other States". Click on Edit (although you probably won't have to change anything here), to see TurboTax's explanation.

This is how many states address the issue of duplicate taxation between states.