Im with HCF and we have family cover plus which covered both babies.

some hospitals are different but, i was private but the twins were public if i wanted them to go private they would have been transfired after birth.

i had an emergancy c sect at 35+weeks my hos i was booked into only took babies from 36 weeks so i was rushed to penrith straight into public, with no choice. but after the first day i got my own room etc.
anyway, i was glad the babies were public cause the work they needed exceeded our cover as it is we still got bills from speciaists. NICU in penrith private costs about $1500 a day. not including other Dr costs. one of the other ladies there said she had her first baby in NICU in private and she paid a few thousand dollars on top of her already OB costs.

in the end i got a private room etc and the twins got the care they needed with little cost. it was win win.