The crash happened just before 10:30 a.m. on I-80 West in Mount Olive Township, with the bus ending up on its side in the grass median with the front end completely torn off.
Photos from the scene:
The identities of the victims were not immediately released, but authorities say one was a child and the other a teacher.
"Our hearts are broken by today's tragedy," New Jersey Gov. Phil Murphy said.
The bus was carrying 38 students from East Brook Middle School in Paramus and seven adults, including the driver. It was headed to Waterloo Village as part of a field trip.
The crash left the bus lying on its side on the guardrail, its undercarriage and front end sheared off and its steering wheel exposed. Some of the victims crawled out of the emergency exit in the back of the bus and an escape hatch on the roof.
Cleanup crews moved the wreckage of the bus Thursday night and I-80 was reopened in the area. Investigators searched for clues and focused on the rear of the bus, the point of impact.
State Police are investigating whether the school bus driver got separated from two other buses, missed his exit, then made an illegal U-turn moments before the bus was rear-ended by the dump truck.
BREAKING: Mount Olive school bus being lifted off I80. Heavy damage to rear half of bus. Two officials briefed on crash confirm that authorities are investigating whether school bus driver made illegal U-turn before deadly crash in New Jersey. pic.twitter.com/mGWEfw9fFh— CeFaan Kim (@CeFaanKim) May 18, 2018
"I heard a scraping sound and we toppled over the highway," said student Theo Ancevski, who was sitting in the fourth row of the bus and was treated at a hospital for cuts and scrapes. "A lot of people were screaming and hanging from their seat belts."
Raw video from the scene:
Around a dozen people remain hospitalized, at least one in critical condition.
"Our thoughts and prayers continue to go out to them as they recover," Bergen County Executive Jim Tedesco said. "This community has been strong, will continue to be strong, come together and support the entire education community."
Two other buses not involved in the accident returned to the school, and students were dismissed early. Tedesco said school will be open Friday, and grief counselors will be on hand to assist the students and staff.
A red dump truck with a mangled front end was parked along the highway nearby. The truck was registered to Mendez Trucking, of Belleville, and had "In God We Trust" emblazoned on the back of it.
Mendez Trucking has about 40 drivers and trucks, according to the Federal Motor Carrier Safety Administration. Its trucks have been in seven crashes in the last two years, none of them fatal, according to FMCSA.
The company was fined $22,850 in 2016 for violating regulations on inspections, repairs and maintenance and post-crash drug and alcohol testing, according to the FMCSA.
Mendez trucks have racked up more than 130 violations in the last two years, according to FMCSA, including 27 for excessive weight, 17 for leaking, spilling or falling cargo and four speeding violations - three of them this year.
The company also has a higher than average vehicle out-of-service rate, which means inspections found violations which had to be corrected before the vehicle could be returned to service. Mendez's rate was 37.9 percent, according to FMCSA. The national average is 20.7.
Officials say the students were wearing seat belts. Both drivers are cooperating with police.
The Paramus Police Department has set up a hotline. Additional information regarding the bus accident can be obtained by calling 888-407-9628. This line will be updated as needed.
(The Associated Press contributed to this report)