Students on the school bus, which had no seat belts, were screaming when rescue workers arrived. "They were thrown all over the bus," said Huntsville Fire Chief Dusty Underwood. Some had to be pulled from the crushed front of the bus.
Two teenage girls died at the scene, and a third died at a hospital, police said. An earlier report had said four were dead.
CBS affiliate WHNT-TV reports the bus was on its daily route to Drake State Technical School, where students can receive special science and math credits.
Police Chief Rex Reynolds said officers were looking for a small car that apparently came close to or struck the bus, causing it to veer off the elevated section of Interstate 565. More than 30 students and the driver were taken to the hospital, he said.
Frantic parents went to the scene, where some students sat dazed or lay draped in white sheets, and went to the hospital to find their children.
Hospital officials said staff members had trouble identifying some of the more severely injured students who were unable to talk and had no identification on them.
Some parents told WHNT their children called them from cell phones as soon as the bus hit the ground, and they rushed to the crash site.
Authorities identified the dead as Christina Collier, 18, Nicole Ford, 17, and Tanesha Hill, whose age was not immediately available.
The police chief said hospital personnel were able to speak with the driver.
Hours after the wreck, a damaged red compact car remained on the interstate near where the bus plunged over the side. But it was not immediately clear if it was the vehicle mentioned by the police chief.
One student told WHNT the accident seemed to happen in "slow motion." A car cut off the bus, and the driver tried to dodge, but hit the car anyway. For a moment, the bus hung on the railing before it fell.
The student was not injured, he told WHNT, "only by the grace of God. When I got off that bus, I got down and prayed because me and my two brothers made it off OK."
He and his brothers were three of about 10 passengers who were ambulatory, a fire and rescue spokesman said.
Parents at the scene told WHNT that their children called them from cell phones as soon as the bus hit the ground, and they rushed to the scene.
A bus company spokesman told WHNT that the driver survived the accident, but has not yet been able to tell what happened. The driver has been with the company for 3½ to 4 years, he said.
The accident occurred near several hospitals and the fire and rescue service station, so first responders were on the scene quickly.
CBS News correspondent Lee Cowan reports that only five states mandate safety belts be installed on new school buses. And none of the laws require students to buckle up.
Crash tests show that school buses react differently than a car during an accident. The government says the best protection is the padding on the back of bus seats, which creates a protective envelope called compartmentalization, Cowan reports.
"They actually tested lap belts, lap shoulder belts and other means of restraining passengers and still felt compartmentalization does the job," Charley Kinnington, of the National Association of Pupil Transportation, tells CBS News.