The partners were asleep in their home on Browning Road, Fox Hill, when two men smashed the glass in their front door to force entry to the property.
One of the women, a 37 -year-old civil servant, jumped out of bed to investigate and was confronted by two men in the hallway at the bottom of the stairs.
As she stood on the landing one of the men approached her from downstairs and pointed a gun at her head while demanding cash and drugs.
Her partner, a 42-year-old community nurse, was also threatened with the firearm while the gunman barked the same demands at her.
He opened the loft hatch on the landing, saw that it was empty and left after being handed £100 the women had in their home.
As the men fled they picked up the keys to the Toyota Yaris parked outside, which the community nurse needs for her job.
The civil servant threatened first said: “I just wanted them to go but how do you prove you are telling the truth when they are asking for weed and you say you haven’t got any.
“I didn’t know what they would do. He was just three steps away from me on the stairs with the gun pointed in my face. I put my hands in the air and was thinking is it a real gun, is it fake, will he use it?” she said.
“We say we are fine physically but we aren’t mentally. We can’t sleep, every noise makes us jump, my partner keeps seeing them in the house and the gun.
“Your home is supposed to be the place where you are safe, but we don’t feel that now. It would help if we knew the police had caught them, so if anyone knows anything, please come forward.”
Her partner said: “I came out of the bedroom and saw the gun being pointed and we were telling them we did not have what they wanted but whoever spoke had the gun aimed at them.
“They got the money but it is the car which hurts the most as I am a community nurse and need it for my job, especially with Covid-19 when nurses are so busy.”
The women said police believe the intruders got the wrong house and that another property in the community is likely to have been the intended target.
Detective Constable Natalie Bettison, of South Yorkshire Police, said: “We are aware that incidents like this can be alarming to our communities.
“We are working hard to identify the men involved in this incident and ensure they are arrested.”
Anyone with information should call 101 and quote incident number 202 of July 11.