NJ is not taxing both your income and your wife's income. It just looks like it is.
NJ will calculate what your tax would be on all your income as if you were a resident. Then they will prorate the amount of NJ tax to the percentage of income you actually earn in NJ.
So if your income from all sources is $10,000 but your NJ source income is $8,000, NJ will calculate the NJ state tax on $10,000 then multiply the total state taxes generated by 80% ($8,000/$10,000). So even though you all your income is being reported on your NJ state tax return, you are only being taxed on the NJ source portion of your total income.