Once you get to Belize City and you want to fly out, you can fly to Roatan, Guatemala City, Cancun Mexico, San Pedro in Honduras, etc. You can fly regionally quite easily out of the International Airport as well.
If you need to fly to Miami, you have to fly an International Caribbean, United, USAir or TACA for that. If you are from the US and you want to fly to Belize, you would need to get yourself an International flight with American Airlines, USAir, United, TACA, and fly into Belize City. The major gateways for Belize from the US include Charlotte, Atlanta, Miami, Houston and LA. Those are all direct flights. Delta just announced direct flights from LA to Belize City. It is pretty good. The tourist demand is there.