I understand the child isn't biologically yours but if your wife is raising the child and you wish to live with her, won't you raise the child as well? How is that so different from having a child (genetics aside)?
Not to mention, the problem here is that she had a child "the old fashioned way" which really puts your relationship in a weird light. If the only problem is that you can't have a child then why not use a sperm donor and do IUI or IVF?
It'd be really hard to convince USCIS that this is a bona fide marriage. USCIS (belonging to the Department of Homeland Security), however has nothing to do with issuing passports (Department of State does that).