It is possible to travel from Belize to Roatan. There are one or two options. Atlantic Airlines fly from Belize City to San Pedro Sula and direct to Roatan. We recommend you check the schedule with Atlantic beforehand.
You could either fly direct to Roatan or an option would be to fly to San Pedro Sula and then travel by bus to La Ceiba, this is a 3 hr bus ride.
Another more adventuress route would be to take a boat from Punta Gorda, Belize to Puerto Barrios in Guatemala. The boat leaves twice daily. From Puerto Barrios you can take a bus to the Guatemalan and Honduran border from there you can get a bus to Puerto Cortes and at times a direct bus to San Pedro Sula. Then it is just a matter of another bus from San Pedro Sula to La Ceiba. This is a long trip and from Punta Gorda to La Ceiba may take 8 to 9 hours, approx. If you where planning to take this route consider stopping in San Pedro Sula to break the journey up abit.