The mother was punched in the face and slashed with a broken bottle after an argument at The Harvester, in Beulah Hill, Upper Norwood.
When the father stepped in to protect her, he was smashed over the head with a bottle.
The couple also claim their children, aged just 6 and 9, were racially abused.
The family, whose identity we have agreed to protect, is asking for help to catch their assailants.
"I can't sleep at night because I feel like my children are at risk that these people might come back," said the mother.
"Someone must know who these people are, so I would just plead with them to go to the police with any information they have.
"I just want to know my family is safe."
The family, who are from the Coulsdon area, went into the Harvester pub Beulah Spa at about 6.15pm on November 13.
They had just sat down when a group of five people came in.
The mother said a woman started the confrontation by suggesting she was looking at her.
When the father tried to defuse the situation, the others in the group began hurling racist abuse, even calling the couple's six-year-old a "white devil".
"It all happened really fast," the mother said. We stood up to leave and the woman punched me in the face.
"We were struggling and someone else smashed this bottle over my head from behind, the pain was blinding."
The mother suffered two black eyes and a cut to her head, while the father was treated at Croydon University Hospital for a gash to the back of his head. He has since returned to work, but has suffered concussion, while his partner has been having panic and anxiety attacks.
"I am scared all the time and I can't think of anything else," she added.
"It was one of the worst nights of my life and I just want to put it behind me."
A police spokesman said officers are investigating the attack, but no arrests have been made.
A spokesman for Mitchell and Butlers, which owns Harvester, said: "This was an isolated yet extremely serious incident which occurred between two groups of customers.
"Our staff called the police immediately to deal with the situation, and will do everything they can to assist with any subsequent police investigation."
Anyone with information can contact Croydon Police on 0300 123 1212 or Crimestoppers anonymously on 0800 555 111.
Not one mention of this on the BBC, or in any of the national dailies.
Also, isn't it rather hard for the public to come forward with any information if they don't know what the assailants look like?
Might be a bit of a sensitive subject, I realise, but still.
Can you imagine the outcry if the reverse had happened? Five skin heads, broken bottles, "Black Devil"?
I think cases like this amply demonstrate that the dreaded sin of racism is alive and well in Britain - and those who denounce it the loudest are the most guilty of perpetuating it.
After all, these people don't matter, they're not part of some special interest group - it's not as if society can learn any valuable lessons from this crime, is it?
Actually, perhaps it can - and perhaps that's why the media do their best to avoid stories like this where possible.