The offenders were said to be using weapons including wooden bats, causing injuries to six members of the family.
The incident happened at around 2.20am on Tuesday (1/1) in an alleyway leading towards the car park in Exchange Street, the alleyway is known locally as Long Lionel.
Thames Valley Police said: "We're appealing for information following violent disorder in Aylesbury which left four people needing hospital treatment.The victims were a family including three men aged 59, 55 and 36, three women aged 55, 53 and 34 and a teenager aged 15.
"They were walking along the alleyway when they were approached by a group of three or four men, who verbally abused one family member before physically attacking the rest of the group.The 59-year-old man suffered a fractured cheekbone and other significant facial injuries requiring reconstructive surgery.
The 55-year-old man suffered a serious head wound requiring plastic surgery.
The 36-year-old suffered a fractured arm and facial injuries.
The 55-year-old woman suffered loss of hearing in one ear.
Four of the victims required hospital treatment and have since been discharged.
One of the offenders is an Asian man, about 5ft 9ins, aged in his mid-twenties. He had short dark hair and was wearing a red coat and blue jeans.
The rest of the offenders were white men. One of these is described as being aged in his mid-twenties, of skinny build, with short dark hair and some stubble or a goatee beard. No further descriptions are currently available.