My husband is a US citizen and his cousin is considering giving her baby up for adoption.

We live in Italy and the child is in California. What are the ramifications for home study or any other ramifications related to the fact that we live in a foreign country?

It may be possible to adopt your husband's cousin's child from California, but this would be an international adoption even though your husband is a US citizen. Italy has signed the Hague Convention on Child Trafficking as has the United States. As a result, you would need to work with an agency in the United States that is Hague Convention Certified. You can find a list of
these agencies at: http://adoption.state.gov/hague_convention/agency_accreditation/agency_s...

In addition, I would suggest that you visit this web site that is maintained by the U.S. Dept. of Health and Human Services. It provides detailed information about Intercountry adoption from Hague Convention and Non-Hague Convention Countries: http://www.childwelfare.gov/pubs/factsheets/hague.cfm