I need to transport my dogs from Honduras to the States. Which airline?

My husband's job posting in Honduras is almost over and we'll be moving back to the States soon. We have 2 labradors that have been with us for years. Their paperwork and vaccinations are up to date, so thats not an issue. In '02, we moved from Miami to Guatemala and the dogs flew on American Airlines - direct flight, no problems. In '06, we moved to Honduras. Now we are moving back to the States. Problem is, we cannot find an airline that will transport an animal over 10 lbs now!!! Or an airline that flies directly from the capital (Tegucigalpa) to Miami or Los Angeles!! We were told airlines only transport animals if it's a direct flight, if they are under a certain weight, and only certain times of the year... Anyone with inside knowledge about traveling/transporting larger dogs please help!!