Gilham was placed on a five-year good behaviour bond for that killing in 1995.
But some of his extended family, particularly his father's half-brother, Tony, were convinced he carried out all three murders and campaigned for him to be prosecuted.
In 2008 he went to court; a first trial ended in a hung jury, a second found him guilty. He was given two life sentences.
Now it was the turn of Gilham's wife, Rebecca, and other family members and friends convinced of his innocence to lobby for justice.
Yesterday about 50 of his supporters were present for the appeal ruling, and they burst into applause as a smiling Gilham left court arm-in-arm with his wife.
The couple have three young daughters.
The prosecution's case collapsed within two days, as the Crown's forensic pathologist, Christopher Lawrence - who carried out autopsies on all three bodies - admitted that carbon monoxide levels in Christopher Gilham's bloodstream indicated he could have been alive when the fire started at the family home in Woronora, in southern Sydney.
That backs up Gilham's claim that it was Christopher, not he, who lit the fire - and, by inference, that it was Christopher who stabbed their parents with a fish filleting knife in a frenzied attack: Stephen 28 times, Helen 17 times.
The appeal judges also heard that after Jeffrey's trial a bloodied fingerprint was found on an intercom, corroborating his story that he was summoned to the house from the nearby boatshed, where he lived, by his mother's cries for help.
Gilham told police that in the months before the killings Christopher, who was having trouble finding a job, had become withdrawn and moody, and prone to fits of rage.
The judges said yesterday that he was entitled to a retrial, but indicated that they might acquit him.
Gilham, who hugged his wife after the ruling, was released on bail after providing a A$100,000 ($130,833) surety and agreeing to report to a police station once a week.