A man wearing a balaclava and pointing a handgun forced his way into the house in Garfield Avenue, Bellshill, at around 9.30pm on Friday.
A 60-year-old man and 58-year-old woman had been in the property when they heard a knock at the door.
The gunman made his way inside when the door was opened and an altercation took place but police said it could have been a case of mistaken identity.
The couple’s 29-year-old daughter and her 30-year-old partner were also upstairs at the time and came down to assist.
The suspect then made off from the house and was last seen in Orbiston Drive.
Detective Sergeant Lorraine Wilson said: “This man barged into a home where two young children were asleep upstairs and threatened the occupants with a firearm.
“Thankfully nobody was injured but it is absolutely vital that we trace this reckless individual and extensive enquiries are ongoing to establish the full circumstances surrounding the incident.
“At this time we have no information to suggest why this home was targeted, and the possibility of mistaken identity is a line of enquiry.
“It would still have been daylight at the time of the incident and I would appeal to anyone who was in the area and may have noticed a man dressed in black acting suspiciously to please get in touch.
“Anyone with information is asked to contact Wishaw CID via 101, quoting incident number 4827 of Friday 25 May 2018. Alternatively you can call Crimestoppers on 0800 555 111 where details can be given in confidence.”