procedure for adopting child of wife who is an immigrant without a green card

I presume that you are a U.S. Citizen. If that is accurate, then your daughter is a U.S. Citizen and your question has nothing to do with obtaining immigration benefits for her. I also presume that your daughter and your husband both are in the United States at this time.

A step-parent adoption will be governed by local state laws, not by federal laws (such as is the case with immigration law). Generally, the biological father's parental rights will have to be terminated, either voluntarily through his signing legal papers to surrender his rights or involuntarily by a court having jurisdiction issuing an order termining his rights (as a result, for example, of "abandonment"). Either concurrently with the termination of the biological father's rights, or subsequently, a petition for adoption must be filed in the court having jurisdiction over the child (most likely in the county where you and she reside). I strongly recommend that you and your husband engage a domestic relations attorney to assist with the important legal steps for accomplishing the adoption, and I send you and your family my best wishes for success.

[Please note that as contemplated in the AVVO Terms of Use, this reply is supplied as general information and is not intended to be legal advice to you. Please do not consider our firm or me engaged as your counsel, with the establishment of an attorney-client relationship, unless and until I may confirm legal representation in writing.]

David N. Soloway
dsoloway@fspklaw.com
Frazier, Soloway & Poorak, PC
1800 Century Place, Suite 100
Atlanta, Georgia 30345