The incident occurred on NH 31 at Zero Mile police outpost near Bathauli village under the jurisdiction of Barauni police station, a police officer said.
The deceased were identified as Ram Uday Tanti (42), his wife Sunita Devi (35) and his sister-in-law Rupmani Devi (38), Zero Mile police outpost officer in-charge, Sunil Kumar Suman said.
All three died on the spot, he said.
The injured children have been admitted to sadar hospital where their condition is stated to be critical, the police officer said.
Traffic movement on NH 31 had come to a standstill for two hours after locals blocked the road in protest against the incident, the officer said.
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