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 said one was a child and the other a teacher.
"Our hearts are broken by today's tragedy," Democratic New Jersey Gov. Phil Murphy said in a tweet.
The bus was carrying 38 students from East Brook Middle School in Paramus and seven adults, including the driver. The bus was headed to Waterloo Village as part of a field trip.
The front end of the bus appeared to be crushed or ripped off, and its undercarriage was completely sheared off. A piece of the front end, with the steering wheel visible, was laying on top of the metal barrier separating the highway from the median.
Raw video from the scene:
Around a dozen people remain hospitalized, with at least one in critical condition.
Two other buses not involved in the accident returned to the school, and students were being dismissed.
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.
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.