The six people inside the truck then fled the scene on foot as good Samaritans raced to help the trapped family.
It happened just before 11:30 p.m. on 6th and Fulton streets in Elizabeth, where the mother was driving for a food delivery service with her twin babies in the backseat.
First responders broke windows get the victims out.
"It was hard," said witness Brian Martinez, who was outside when it happened. "They had to break down the sunroof and then the back windows, because we didn't want any glass to get into the babies, that is a bit dangerous."
The children were said to be in child safety seats in the back of the SUV.
Martinez said he believed the children were OK.
Police say the investigation is ongoing and that they've identified the driver of the pickup truck
At this point, it is unclear what charges have been or will be filed.
ALSO READ | Police: Unlicensed driver facing charges in death of teen on dirt bike in New Jersey
* Get Eyewitness News Delivered
* More New Jersey news
* Send us a news tip
* Download the abc7NY app for breaking news alerts
* Follow us on YouTube