The 2005 Honda Odyssey minivan they were riding in was hit by a freight train near the Euclid Avenue train crossing around 1 a.m., police said.
The Lake County Coroner's Office has identified the victims as Pedro Trinidad, 36, Flor Carillo, 38 and Evelyn Trinidad, 5, all of East Chicago.
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The three other children are hospitalized and said to be in critical condition.
Surveillance video shows the driver of the minivan ignored an activated train crossing signal and drove around a crossing gate when the vehicle was hit, police said.
The train pushed the minivan about 200 yards west of the crossing.
Authorities have not yet released the relationship of the victims.