You cannot be held personally responsible for any tax issues which occured prior to your marriage. However, if your husband owes back taxes for prior years, if you file a joint return with him, the IRS will withold any refund that the two of you have coming to satisfy his tax debt.
You can avoid this by either filing separately, or if you file a joint return then you should also file Form 8379 for Injured Spouse. By filing this form the IRS would still issue a percentage of the refund which pertains to your percentage of the income.
The only other thing to be concerned about is that any time that you file a joint return, each spouse becomes collectively and individually responsible for the tax liability for that year. So you would want to make certain that any return you file jointly with your spouse is an accurate accounting of your affairs. If the IRS were to discover errors on that return or find that income had been under reported, you would both be held responsible for that tax bill.
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