A bag of rubbish was set on fire at the door of the property in the Spelga Park area of Lurgan at around 4am this morning.
Five crew members from the Northern Ireland Fire and Rescue Service made their way into the property to alert the family - two adults and five children - and led them to safety.
Smoke damage was caused inside the house and to the front PVC door in the attack.
Detectives in Lurgan have appealed for witnesses to come forward.
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