Disney Cruise Ship Rescues Family From Sinking Boat Off Bermuda, New Video

A group of people on a sinking ship in the Atlantic found themselves in the happiest place on Earth ... in the middle of the ocean, after they were rescued by a Disney Cruise Line ship. New video released by the U.S. Coast Guard shows the dramatic Sunday rescue.

Four people were sailing on a 50-foot catamaran called The Serenity, about 230 miles off the coast of Bermuda, when they ran into trouble.

A married couple, their daughter and a cousin radioed for help after a malfunction in the craft's escape hatch caused the craft to start taking on water and begin sinking.

The Disney Treasure -- the newest cruise liner in the company's fleet, en route to Port Canaveral, Florida, from the Netherlands -- heard the call and responded ... it was about 80 miles away from the distressed catamaran, and got to the sinking craft within an hour.

New Coast Guard video shows a lifeboat launched by the cruise liner motoring toward the catamaran -- all 4 onboard the catamaran were rescued safely, and no injuries were reported.

The oldest person on the catamaran was 74, and the youngest was 24, according to a Coast Guard official ... who said they might still be floating out there if the cruise liner hadn't luckily been so close by.

The 4 people on board the ship had a plan in place and were ready to "float," according to the official, before they were rescued. The whole ordeal took place about 1,000 miles east of the Florida coast.

The Disney Treasure, which has 15 decks and more than a thousand staterooms, is scheduled to make its debut voyage with passengers in December.