Mohammad was told to inform his family that he was going to work in Germany and given an Iraqi passport.
Yousef tried to enter with a false Iraqi passport, claiming political asylum.
The Iraqi passport is issued to citizens of Iraq for international travel.
He was holding an Iraqi passport but no American visa.
She became a United States citizen in 1987 but held on to her Iraqi passport, which has long since expired.
Counterfeit driver's licenses, teaching certificates and even Iraqi passports, with or without visas, are available for up to $800.
"It's a bad time," said one American official, "to be flying around the world with an official Iraqi passport."
It said the men carried Iraqi diplomatic passports.
She became an American in 1987, although she retains her long-expired Iraqi passport.
Using a false Iraqi passport, he asked for political asylum, and was released pending a hearing.