An Australian woman has miraculously given birth to conjoined twins with one body and two brains despite doctors initially telling them to terminate the pregnancy.

Renee Young and Simon Howie, of Tregear in Sydney's west, welcomed their daughters on Thursday six weeks before they were due, the Daily Mail reported.

The couple, who found out via an ultrasound that the twins they were expecting was in fact one child with two symmetrical faces and two brains connected by the one brain stem, said doctors were shocked by the girls' exceptional progress.

'They are breathing perfectly on their own and feeding,' Mr Howie said.

Ms Young gave birth to the girls, named Faith and Hope, via an emergency caesarean at Blacktown Hospital last Thursday.

The girls were born with a rare condition called diprosopus, which means they share the same body and vital organs but have their own faces and brains which are connected by only one brain stem.

'Even though there is only one body, we call them our twins. To us, they are our girls and we love them,' Mr Howie said.  

The condition is so rare that only 35 cases have ever been recorded and none have survived.

Due to the incredibly complex nature of their condition, doctors are so unsure about what to expect from the twin’s condition that they are being forced to make their prognoses day by day. 

From as early as 28 weeks into Ms Young’s pregnancy, specialists were concerned about grave developmental issues.

One of the biggest predicted survival risks from their doctor Greg Kesby, was that the babies would be unable to breathe on their own.

The couple, who are parents to seven other children, were also told early on in the pregnancy not to keep the child ‘because it would be looked upon by the public as a freak’.

They defied the doctors because Ms Young had never terminated a pregnancy and because they had a family 'that gives us a lot of support'.