Thomas Galloway torched the mattress after accusing his wife of cheating on him, Carlisle Crown Court heard.
The family managed to escape unhurt in the early hours of 17 April, but the Carlisle house was badly damaged.
Galloway, 22, of Thomas Street, admitted arson with intent to endanger life and was jailed for five years.
The hearing was told the defendant had been drinking before the attack and was suffering from depression.
Det Con Fiona Murray, of Cumbria Police, said: "Galloway knowingly put the lives of his wife and children in danger due to his actions.
"Thankfully no one was hurt, however this incident could have easily ended in tragedy.
"Justice has been served and I hope it gives the victims the opportunity to move on with their lives."
An arsonist has been jailed for setting fire to his bed while his wife was in it and while three young children were in their house.