No, one is not responsible for unpaid taxes (and generally any other debts) of their spouse that were due prior to marriage.
If you have signed a joint return you usually can be held liable for all of the balance due on that return. Generally, joint and several liability applies to all joint returns. This means that both you and your spouse are liable for any tax shown on a joint return plus any understatement of tax that may become due later. This is true even if a divorce decree states that a former spouse will be responsible for any amounts due on previously filed joint returns.
You and your new spouse can still file a joint return adn not have hime suffer due to your past debts. Form 8379 at http://www.irs.gov/pub/irs-pdf/f8379.pdf can be used for an injured spouse.There may be an injured spouse if you file a joint tax return and all or part of one spouse's portion of the overpayment was, or is expected to be, applied (offset) to the other spouse's legally enforceable past-due federal tax (or state income tax, child or spousal support, or a federal nontax debt, such as a student loan).
File Form 8379 when you become aware that all or part of your share of an overpayment was, or is expected to be, applied (offset) against your spouse's past-due obligations. You must file Form 8379 withe the moint tax return for each year you meet this condition and want your portion of any offset refunded.
Since New York is not a community property state it will not be possible for collection action (liens and levies) to apply to his own property. In cases where one spouse has legally enforceable past-due debt you may wish to consider using seperate accounts for the earnings and assets of that spouse so that comingled assets are not encumbered by any collection action in error.
I hope this is all the information that you need. Please ask if you have another question.