Yes, you can file jointly for NJ and NY returns as well.
For NY, you have to file jointly if you filed your federal return jointly. You'd file as a part-year resident so that only the NY resident spouse's income is included on the return.
For NJ, you can choose to file separately or jointly. If you file separately, only the NJ resident spouse's income is taxable to NJ. If you choose to file jointly, both spouse's incomes are taxable to NJ. However, you may qualify for a tax credit in NJ for the tax paid to NY on the NY resident spouse's income.