05/10/2012 02:35 EDT | Updated 07/10/2012 05:12 EDT

Toddler on no-fly list and parents ordered off plane

An American couple of Middle Eastern descent say they and their 18-month-old daughter were asked to leave a JetBlue plane in Florida because they were told the child is on a no-fly list.

The incident happened Tuesday night at an airport in Fort Lauderdale, Fla., as the family was preparing to fly home to New Jersey, WPBF 25 West Palm Beach reported.

A JetBlue employee told them they had to leave the plane and that an agent with the U.S. Transportation Security Administration (TSA) wanted to speak with them.

"He said, 'Well it's not you or your husband — your daughter was flagged as no-fly,'" the girl's mother recalled.

"The whole situation was bizarre," she told the TV station. "It made absolutely no sense."

They were allowed to re-board the plane about 30 minutes later, but they refused, saying they were too embarrassed to fly on the airline.

The couple's young daughter, Riyanna, has been on planes several times before, and even has her own frequent flyer card.

Her parents asked that they not be identified. All three members of the family are U.S. citizens and were born and raised in New Jersey, WPBF reported.

The girl's father said he thinks they were targeted because the family is of Middle Eastern descent and his wife wears a head scarf.

"We were humiliated, we were embarrassed, we were picked on," he said.

The airline said the TSA was responsible for the incident, while the TSA said the airline was to blame.

Both JetBlue and the TSA said they are investigating.