Jessica Simpson and Tony Romo fly coach

Jessica Simpson and her beau Tony Romo boarded a short American Airlines flight from San Jose, California to Los Angeles Saturday -- and sat in coach just like everybody else, according to an eyewitness.

"A passenger two rows ahead of them was a Cowboys fan and he asked the flight attendant to give them drinks from him," said the source. "They accepted and each had a beer."

"Jessica looked totally bored on the flight," the witness adds to Us Weekly.

After the plane touched down, the couple reportedly waited until everyone got off the 44-seater aircraft before leaving -- and Simpson, 27, thanked the crew and pilots.

"They were really sweet on the plane," said the witness. "About 20 minutes later, I saw Jessica waiting outside the men’s room for Tony, just like any other regular spouse or girlfriend would wait for their husband or boyfriend."