A Qatari appeals court last month cleared Matthew and Grace Huang of involvement in the death of their adopted daughter Gloria, who was born in Ghana.
The Huangs were arrested in January 2013 on charges of starving Gloria and spent nearly a year in jail in Qatar.
The pair's child-endangerment convictions were subsequently overturned and they were allowed to leave Qatar and return to Los Angeles last week.
In the suit, the couple, who are of Asian descent, alleges that MWH Global, based in Colorado, failed to provide security or cultural training to help them survive in a country where mixed-race families are not accepted, the L.A. Times reported.
The newspaper said the lawsuit, filed in Los Angeles Superior Court, accuses MWH Global of negligence, wrongful termination and infliction of emotional distress.
It added that Matthew Huang said in the lawsuit that he was physically and sexually attacked in prison, and that the two continued to fear for their safety after they were released.The couple, who say they were left more than $2 million in debt by the case, claims MWH Global abandoned them and forced Matthew Huang to quit his job, the lawsuit says.
In a statement published in the Los Angeles Times, MWH Global said it was "disappointed" by the lawsuit and had provided immediate and generous assistance within hours of the Huangs' detention.
It said it spent hundreds of thousands of dollars on Matthew Huang's criminal defense.
"MWH met with U.S. Embassy officials, helped arrange legal counsel, checked in on the welfare of Matt and Grace and their children and attended initial court hearings," the statement said.
The company added that it offered Matthew Huang a leave of absence so that he could return to work when his legal issues were resolved, but that he decided to resign.
Matthew Huang had been working in the Middle East nation as part of infrastructure improvements for Qatar's hosting of the 2022 World Cup.
