The family, whose principal member has only been named as Rodney Morgan, were said to have asked management at the Ritz Carlton in Naples, Florida, they did not want to deal with "people of colour" or staff with "foreign accents".
Legal papers state their request was then entered into the computer system at the five star hotel before a black waiter was then stopped from serving them.
The race row came after lawyers acting for the waiter, Haitian-born Wadner Tranchant, sued the hotel.
The 40 year-old black waiter claims he was stopped serving the family during their stay in February to avoid upsetting them.
The rest of the family, who were British, were not identified.
The Morgans had a daughter with them and ate stone crabs and dover sole.
Further details about the family were not disclosed.
According to the lawsuit filed against the hotel, managers breached the Civil Rights Act by stopping Mr Tranchant serving the couple. One of his duties was to fillet the sole at the table.
Mr Tranchant, a US citizen, was so offended he has sought medical and psychological help, according to the court papers. He is claiming compensation.
"On or about February 28, 2010, the Rodney Morgan family arrives as guests of (the) Ritz and specified… their preference to not be served by 'people of colour' or with 'foreign accents'," said the claim lodged at the Florida District Court.
"This preference was entered into the computer system of (the) Ritz at the direction of the (the hotel's managing director Edward Staros) with the further notation '… as per Mr Staros this couple is very very prejudice [sic] and do like like [sic] ppl of colour or foreign accents'."
Michael McDonnell, the waiter's lawyer, said that nine other staff members at the hotel have said they were told the British family did not want to be served by blacks or anyone with an accent.
His lawyers have cited the Civil Rights Act of 1866, which was passed a year after blacks were freed from slavery following the end of the American civil war, which makes it illegal to discriminate in jobs and housing on the basis of race.
A spokesman for the Ritz-Carlton refused to comment.
The case is due in court at a later date.
