No, you may only claim from either Medicare or a Private health fund for each session.  Private Heath will not contribute towards the ‘gap’ between the Medicare rebate and the consultation fees.  Your receipt will have a code specific to either Medicare or Private Health depending on your requirements.

Some private health funds cover psychology sessions.  The benefit payable to members of private health funds varies according to the level of ancillary or extras cover.   It is best to contact your provider directly to check your eligibility and for the rebate information.