Under the scenario you present, custody of your child would be with the natural (biological) parent, and not your husband.
Has your husband considered adopting your child? To do so would require the consent of the natural father. If your husband adopted, the natural father would no longer owe an obligation to pay support.
____
Quote:If you were to write a living will than if something was to happen to you the courts would have to consider your request but they are allow to make thier own decision on what would be in the best Interest of the child.
Note: A "Living Will" (also known as a "Declaration" or "Advance Directive") is not to be confused with a "regular" Will. A "Living Will" is more similar to a Power of Attorney than a Will, and its purpose is to allow you to make decisions about life support and directs others to implement your desires in that regard. It would not be used to state your wishes for care, custody, or control of children.