Maybe it differs by state, but I'm not sure why you even have a social worker involved
. My dh also adopted my biological son and we didn't have to have a homestudy. They did require that he live in the same house for 1 year, and dh had to have an FBI background check done.
However, I would STRONGLY recommend that you tell your son the truth about your husband not being his biological father. My son is almost 9 now, but has always known that my husband adopted him. My 2-yr-old, who is also adopted, will always know. We talk about it openly -- they CAN handle it. The sooner you tell him, the better. You don't want him to find out down the road and KNOW that you've lied to him his whole life and wonder what else you might not have told him.