Ms Rafi said the family applied for a humanitarian visa on August 26 and followed up with the Immigration Department on several occasions to try and expedite the visa process.
Ms Rafi said the interpreter was on the Taliban's notorious "kill list" and was murdered for his connection to the Australian Army.
"Unfortunately, we lost a human being who's served and helped the Australian Army and Afghanistan army, and he's executed now and his family is in a desperate situation," she said.
When the Australian government was in the process of evacuating people from Afghanistan in late August the interpreter and his family were unable to flee the country.
The Australian government is assuring Afghans who worked with the ADF they are being given "the highest priority in the humanitarian program" — but many say they their lives are at risk.
The Australian government has so far allocated 3,000 places within its humanitarian intake for this financial year, but more than 10,000 Afghans are estimated to have applied for the visa program since the fall of Kabul.