The children attend special needs classes at Gower West Elementary.
Their parents say the abuse began last October and continued into January.
The driver allegedly rearranged his route so that he could be alone with the twins.
The Department of Children and Family Services investigated the matter and found there was "credible evidence to the claim."
The driver, school district and bus company are all named in the lawsuit.
The family's attorney hopes this case can lead to changes statewide.
"We want to push legislation very hard requiring some sort of electronic monitoring or some permanent type of monitoring on special ed buses," family attorney Antonio Romanucci said.
The DuPage County State's Attorney says that office is aware of the allegations but no charges have been filed.
The school district did not have a comment on the lawsuit.
