The masked thugs - one armed with a gun - cornered the 49-year-old and his 17-year-old daughter after forcing their way into the property.
Police said the targeted attack took place at the family's home in Glen Avenue, Largs, at around 11pm on Sunday.
Officers said the suspects "knew what they were looking for" and managed to steal a five-figure sum of cash and personal items.
Police said no shots were fired before the culprits made off in a getaway car.
The balaclava-clad robbers are both described as 5ft 10in tall, of slim build, and wearing dark clothing.
Detective Sergeant John Deans, who is leading the investigation, said the family were left terrified by their ordeal.
A CCTV trawl, conducted by detectives at Saltcoats CID, is now under way in a bid to find out more about the suspects.
Police believe the suspects may have made off in a waiting car and are keen to trace anyone who may have seen anything suspicious.
DS Deans appealed for any neighbours, or local residents, who say the two men - or the getaway car -to get in touch with him.
He said: "Thankfully no one was injured but it was a terrifying attack on the man and his family.
"However, we do believe that it was very much a targeted attack as the men involved knew what they were looking for.
"It is possible the men made off in a waiting car, we are checking CCTV and doing door to door in the area to establish this.
"However, I would appeal to anyone who was in the area, who may have seen something suspicious - maybe the men or the car, prior to or after the robbery - to contact police."
Anyone with information is asked to contact Police Scotland on 101.