The twins, Hope and Faith, also share a heart, body and limbs.
Parents of the twins, Renee Young and Simon Howie, said the babies are in good state of health since their birth Thursday last week, according to the local daily Telegraph.
The couple, who have seven other children, said that although the babies share the same body, they consider them as their twins.
"I and Simon think they are beautiful, this is what really matters," the mother said in an interview broadcast Monday night by the Australian Channel 9.
The mother also said that the anomalies of the girls were discovered during the pregnancy and they may die.
Glenn Gardener, a specialist of complicated pregnancies, said that the conjoined twins generally have common chest or abdomen, but in case of Hope and Faith, it is difficult to make a long term prediction and know how their brain will function.
Till date, in the entire world, only 40 cases have been registered of people being born with two faces, a disorder known as Diprosopus or Diprosopia, but very few have survived after their birth, according to the Australian newspaper.
Michael Permezel, president of the Australian and New Zealand College of Obstetricians and Gynaecologists, said the birth of the conjoined twins is very rare.
About one in 30,000 to 50,000 pregnancies produce a conjoined twin, which is the result of an incomplete embryo, but only one in 200,000 makes it to birth.