What happened to me if my husband has a lot of debts, we are separated at the moment but no divorce. Am I responsable for that debts?

The answer is "maybe." Certain debts incurred for basic support (such as food and medical expenses) may be deemed "necessaries," and you may be responsible for them to the vendors under state law. Moreover, in connection with a divorce, the court has the power to require you to pay a share of debts incurred by your husband during the marriage, even if they are not in your name.