The parents are seeking $30 million for the March 2012 incident that the superintendent of Monmouth County's Long Branch School District dismissed as "a joke gone bad," phillynews.com reported Tuesday.
Janitors Kevin Garifine and Robert S. Rego were doing maintenance work in the bathroom when the incident took place.
The suit accuses the two men of tying the boys' hands together with tape and placing tape over their mouths before photographing them with cellphones.
When the boys got back to the classroom, the teacher ignored their account of what happened and the principal failed to call police, the suit said.
The parents allege in the suit as a result of the incident their children are depressed, suffering from post-traumatic stress disorder and unable to sleep normally.
The school district did not immediately return calls seeking comment, phillynews.com said.