Both you and your wife will definitely need valid passports on arrival in Honduras. Does she have a UK/Irish passport? If so, this should do if it is not expired and has at least six months left on it on arrival in Honduras (yours too).
My wife is from Honduras. We finally got through the INS interview process and she has her permanent residency card. If your wife does not, make sure she has appropriate travel documents from INS to get back in to the USA or getting in to Honduras will be the least of your problems.
For travel to Roatan San Pedro Sula (SAP) is your best/closest destination in Honduras, not Tegucigalpa (TGU). Much safer airport too.
Charlie Meador, La Ceiba, Honduras