A device was put through the letterbox of the property at Carlisle Parade on Thursday shortly before 10pm.
It was found when a noise was heard at the front of the house.
A family member reacted quickly, throwing the device into the front garden, a police spokesperson said.
A number of homes were evacuated by police on arrival. Army bomb experts made the device safe.
The couple escaped with their children, aged two months, two, four and 11-years-old.
Detectives said the culprits showed no regard whatsoever for the safety of the family and their neighbours, seriously endangering their lives.
They are asking anyone who may have witnessed the incident or who has any information to contact them.
Local Sinn Féin councillor JJ Magee said: "At the scene late last night I saw people having to leave their homes with children being lifted from their beds and for what?
"Whoever was behind this alert should explain to local residents what they have achieved by forcing families from their homes.
"The people of this area want to get on with their lives and trying to improve the future for their children without criminal elements causing distress and inconvenience."
It is the latest viable device found during a series of security alerts in the region this month.
Police investigations are ongoing.