First, YOU don't have any custody of the child since you are not the biological mother. So, at the start, this has nothing to do with you. Also, was your husband married to this woman? I'm assuming not. The problem here is this - if they weren't married, then, technically, your husband has no legal rights to the child at all - birth mothers receive sole legal and physical custody at birth. Has your husband ever gone to court to obtain a custody order before? Was he ever ordered to pay child support? Is he on the birth certificate or was a DNA test ever performed? These are all relevant issues because, in order to even launch a custody petition, he has to prove he is the biological father. Being on the birth certificate at least creates a presumption of parentage, although a DNA test will probably have to be done.
Once his paternity is established, he can ask for sole legal and physical custody. That, however, will not terminate the mom's rights, and YOU cannot legally adopt the child as your own until her rights are terminated. Unless she voluntarily agrees to that plan, they probably won't be terminated, so no adoption can ever occur. Also, the mom would be liable for child support, and most courts won't let you simply say, "That's okay....no need for it," since it is for the child, not you. You may be required to obtain a support order if the custody change occurs.
Consult with a local family attorney ASAP.
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You need to hire an attorney. There is no guarantee that the biological mother will not see the child. A qualified family law attorney can help you. Please do not try this alone.