I was recently surprised by having my checking account garnished because of an old debt that my husband owed. This debt was created before we were married. Do I have any rights in this regard?

If the bank account is in both your names, no, I don't think you can change the situation. He should have made you aware of this, and it has to be expected because they just don't walk away from people owing money to them.

If the account is in both names, they can take all of "HIS" money out of it, if you had money from your earnings in it, you can petition the court to release those funds, but you will have to prove what part of it was your money

You can file a Third Party claim against he account with the court, as long as you can prove the funds are yours, the court will release them.