Fire crews from Bracknell and Wokingham were called to a property in Ennerdale, Wildridings, at 1.54am.
Firefighters spent two hours extinguishing the bin fire, which had spread from the bin store attached to the house to the porch and just inside the front door.
One hose reel was used, while two firefighters used breathing apparatus to enter the house.
They spent the rest of the time dampening down hot spots.
Bracknell Forest Council have boarded up the property while police investigate the cause of the fire.
The parents and two children have since arranged to stay with relatives.