He said Henry was made to feel "like a criminal" in front of other passengers and was detained by about an hour to be questioned by authorities.
"This is not how anyone deserves to be treated," Joel said. "This is not something that should have happened in front of my son.
"This is not something that anyone should have to worry about happening to them on a flight just because someone might not like the looks of them."
Joel said he and Henry were foster parents and were in the process of adopting their second son.
"This misguided [flight attendant's] assumptions about my husband and the accusations that he made are completely unfounded and we plan on getting up bright and early in the morning to make as much f**king noise about this as I possibly can," he said.
Joel added: "This is the icing on the cake for a man who has spent nearly the last two weeks in Puerto Rico dealing with his father's quick decline and subsequent death."
Since the story went public, United Airlines has issued an apology to the couple.
"Our customers should always be treated with the utmost respect," United spokesman Jonathan Guerin said in an email, published by the News & Observer.
"We have followed up with the customer directly and we apologised for the situation."
The couple are now said to be seeking "fair compensation", the News & Observer reports.
The family's ordeal is the latest in a string of incidents involving parents wrongly accused of in appropriate behaviour with their children.
Last month, in another incident involving United Airlines, a Mexican father was accused of child trafficking his own daughter because his fair-skinned offspring "didn't look like" him.
The girl's mother, who is of Irish descent, said she "burst into tears" when she was called by an official from the New York Port Authority to verify her husband's story that their three-year-old girl was in fact his child. The airline apologised to the family over the incident.
Also in April, a father in the UK was accused of paedophilia when he checked into a hotel with his 13-year-old daughter.
Widower Craig Darwell, 46, was treating his daughter Millie, 13, to a trip to an amusement park when he checked into the TraveLodge hotel.
The hotel later apologised but a spokesman said the company took its "responsibilities towards protecting children and vulnerable young people extremely seriously."