The arson attack took place on Bishopscote Road in the early hours of Monday, December 2, shortly after midnight.
The offender, described as a man wearing a hoodie, was spotted dousing a substance over the family's car and garage before fleeing the scene.
Residents of the address included an elderly couple and young children, all of whom were forced to escape from their home in the middle of the night.
An eyewitness said: "Calls were made to police as people heard loud explosions and were woken up by the bang...
"The flames reached as far as the upstairs and fire crews fought the blaze before they got it under control.
"Police stayed all night long and forensics came the next day."
The source called on Luton's politicians after the upcoming general election to be tough on crime, adding: "What are they going to do about this?"
A Bedfordshire Police spokesman said: "We were called at around 12.30am on Monday, December 2, to reports of a fire in Bishopscote Road, Luton.
"A vehicle had caught fire, which spread to the front of a nearby property. Officers are investigating the incident as arson endangering life.
"Anyone with any information is asked to contact police on 101, quoting reference 40/69518/19."