If you file separate returns, you will not be responsible for his back taxes.

You could also file a joint return and include Form 8379 Injured Spouse Allocation.  This will protect your portion of any refund from being used to satisfy his obligation and give you the benefit of the better tax rules for joint returns.  The only disadvantage of this is that it will take much longer for you to receive your refund, about 12-16 weeks.