You should check with your charter operator for details.
The great Blue Hole (just a little over 400 feet deep*) lies approximately 60 miles off the mainland (out of Belize City), and is part of the Lighthouse Reef System.
http://ambergriscaye.com/maps/art/belize_mapBIG.jpg
* The dive exceeds the depth limit of an Open Water Certified Diver - technical training required to go to the bottom.
Several PADI operations service the Blue Hole, both out of Ambergris Caye or Belize City (check out
PADI. The Way The World Learns to Dive). Peter Hughes' Sun Dancer II (
Dancer Fleet - Peter Hughes Diving) and the Belize Aggressor III (
Aggressor Fleet | The ultimate in live-aboards since 1984) both include it in their weekly itineraries.