The driver of the car, Maria Barrteo, 36, of Astoria, N.Y., is listed in critical condition at Duke University Medical Center.
According to the Highway Patrol, a passenger was apparently passing Barrteo a cup of coffee when she veered off the road and lost control of the car around 12:05 a.m. in a northbound lane.
Troopers said the car flipped at least eight times, ejecting two of the children.
Jaslynn Barrteo, 1, Luigi Barrteo, 3, and Franklin Rivas, 2, are listed in good condition at Cape Fear Valley Medical Center.
Jorge Barrteo, 37, Jorge Bartteo, Jr., 11, and Byrone Rivas, 13 were treated and released.