Canberra: A Bhutanese family who have lived and worked in Australia since 2012 are appealing to the immigration minister to give them permanent residency after it was refused because their deaf son would be a “cost” to the taxpayer.

The Wangchuk family live in Queanbeyan, in New South Wales, and are facing deportation this month unless the immigration minister, David Coleman, uses his discretion to grant them visas.

The family came to Australia in 2012 so the mother, Jangchu, could study in Melbourne, after which they moved to NSW.

In March the administrative appeals tribunal upheld a decision not to give the family permanent residency visas.

The tribunal member, Jennifer Cripps Watts, found the family did not pass the public interest requirement of the visa process, which stipulates the applicant be free of a disease or condition which would likely require health care or community services which would likely “result in a significant cost to the Australian community in the areas of health care and community services”.

“I know my son is deaf, but it’s not that he’s going to incur a huge amount of spending of taxpayers’ money,” Jangchu Wangchuk told Guardian Australia.

“He’s just deaf and uses a hearing aid and he never has any ongoing treatment or medication or anything. My husband and I are working so hard, and we are paying taxes. We have a very stable jobs and we love our jobs.

— Guardian News & Media Ltd