The family also alleged in the suit that the school cost them "at least $250,000" for "fraudulent misinterpretation."
The family and the school district would not answer specific questions about the lawsuit, but offered prepared statements on the case to ABCNews.com.
"The Heinemann family is deeply disheartened by The Cathedral School of St. John the Divine's actions and request privacy while they try to resolve this issue and protect their children," the family spokesman, R. Couri Hay, said in a statement to ABCNews.com.
Randy Friedberg, the family's attorney, did not respond to ABC News' requests for comment.
The Cathedral School called the family's suit "sad, false, and without merit," a school spokesman said.
"The Cathedral School has a more than 100-year reputation of excellence in education and service to its students and demonstrates a profound respect for the dignity and equality of every child," the spokesman said in a statement.