I went in as a private patient, with a private Ob, in a public hospital. My PHI didn't cover private hospital for pregnancy.
I only had to pay for my Ob (naturally). Everything else, including the epidural was covered. I did get a private room as there was one available on my admittance, and most will give you two parking tokens / newspapers etc
If you are looking at having a private Ob, check that they birth at your chosen hospital - there are quite a few Ob's here that won't birth in the public system

In regards to the excess, apparently the hospital will send the bill to the PHI and they will determine if they cover the whole expense, or if you have a gap to pay (that's what I was told anyway)

Good luck