Louise Cheyne, 35, her husband Martin, 37, and four young sons had to shelter in a neighbour’s house while fire crews tackled the blaze.
Their blue BMW 220 and the grey Vauxhall Corsa were also destroyed in the incident in Sandhaven, Aberdeenshire, in the early hours of yesterday morning.
Police have launched an investigation and confirmed it the fire is being treated as deliberate.
A fire service investigations unit has also attended as part of the inquiry.
Lousie, a nursery practitioner, said the family had been woken by the blaze. The 35-year-old said the ordeal had been “terrifying” and took her four young sons, aged between 11 and two, to a neighbour’s home as firefighters battled the flames.
She said: “We’ve got four kids under the age of 11 and it was quite scary. It’s just out of the blue because Sandhaven is just a quiet wee village.
“We want the people who did this to know that this isn’t on.”
Louise said the incident has left her children “shaken” and warned the fire “could have been worse”.
She said: “We had one car parked in the drive and the other one was opposite the house. We also have a woodshed and they have tried to set that alight as well.
“We sent our three oldest boys to school but they are aware that cars don’t just go on fire, so they were a wee bit shaken. Nobody has been hurt though and it could’ve been worse.”
Martin, a mechanical fitter, added: “We had to flee because we didn’t know what was next. There were two gas tankers just yards from the fire.”
Detective Sergeant Martyn Thomson said: “Inquiries are currently ongoing into the fires which we are treating as having been started deliberately.
“Thankfully no-one was hurt but had the fires not been noticed so quickly, the outcome could have been much worse. I would appeal to anyone with information to come forward.”
The fire service said it had been called to Sandhaven at 2.47am.
Crews from Fraserburgh took a little over half an hour to fully extinguish the blaze.
Anyone with information that could assist with inquiries is asked to call police on 101 or Crimestoppers anonymously on 0800 555 111.