My name is NOT on the title of our house, though married. I were to have an enormous debt, can they come after my husbands house for my debt

If you were married at the time the house was bought, you may have Dower Rights in the property. If he had the home prior to the marriage, the home should be safe from your individual creditors. Michigan permits marital estates in land which are usually (with some exceptions) judgment proof except to jointly created debts (like mortgages).