Image copyright Lindsay Gottlieb/Twitter Image caption Lindsay Gottlieb and her fiance were asked to prove their son was theirs despite having his passport

Southwest Airlines has apologised after one of its employees asked a California basketball coach to prove that she was the mother of her bi-racial son.

Lindsay Gottlieb, who is white, and her fiance Patrick Martin, who is African American, were both present and showed the official their son's passport.

She says after showing his passport she was asked for further evidence through a Facebook post or birth certificate.

The airline said it would use the incident to "coach" employees.

Ms Gottlieb, who is the head coach of the University of California, Berkeley women's basketball team, called the incident "demeaning and insensitive, not to mention inefficient" on Twitter.

"I'm appalled that after approx 50 times flying with my 1 year old son, ticket counter personnel told me I had to 'prove' that he was my son, despite having his passport," Ms Gottlieb wrote.

"She said because we have different last name. My guess is because he has a different skin colour."

According to Southwest Airlines' policy, customer service agents must verify a child's age at the airport using a government-issued photo identification, but there is no regulation regarding matching last names of a child with the accompanying adult on domestic flights.

Airline officials said in a statement the company had contacted Ms Gottlieb and apologised "if our interaction made this family uncomfortable", the Washington Post reported.

Image copyright Lindsay Gottlieb/Twitter Image caption Lindsay Gottlieb (left), son Jordan (centre) and her fiance Patrick Martin (right)

Ms Gottlieb told a CBS News affiliate she did not feel the issue was an airline-wide problem, but "just one insensitive employee".

"It hurt my feelings," she said. "It made me feel a little bit less than and it's not OK."

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Ms Gottlieb and Mr Martin's son, Jordan Peter Martin, has travelled frequently - and often on Southwest Airlines - with his mother's basketball team.

Later, Ms Gottlieb wrote on Twitter that her family was fine, but that she suspected these incidents were "much more common" for non-white parents.

"I do feel like as a white female, with a position of privilege, and a platform where someone is going to listen, it is my responsibility to say, 'hey, this happened, this isn't OK,'" she told CBS News.

"And maybe somewhere down the line, that helps my son, who is biracial and will be for his entire life."