There are no rules. OR there are too many rules, depending on how you look at it. I know.... Not great help. So child support is assessed based on income and care %. IT has nothing to do with the mortgage / rates / water / house insurance / personal loans / car rego etc etc. That is all laid out in a realm of law called family law. It is complex but the simple version for you is this. His income and your income are calculated and run through an equation that factors in the age of the kids, how many kids and how the care %. You have 100% care right now. So child support has assessed his child support liability is $550 a fortnight. Done and dusted.
But the child support agency are not interested in who paid the rates / mortgage or anything else.
But you're also messed up with contract law and property law and property law is messy because it is intertwined with family law. The fact is your name is on the title and the mortgage. So according to contract law you have a responsibility to the bank. You have a contract with them. Now what about property law? well what happens with asset division because family law and property law get mixed together here if you know what I mean? So IF the ex pays everything from now until the house sells then he has a good argument to see some additional funds come back his way when the house sells.
So here is the real issue... Any property settlement between you and the ex that is legally binding in family law requires you both to get legal advice. Some folk do manage to just sell everything, come to an agreement and save spending a fortune on solicitors.
My advice - get child support to collect. Save all the $$$ that could / should be paid and keep it in a bank account he cant access. If thing go nice, then great, if not, you're gonna need that money for this horrible game called family law. Obviously, stuff is stressful atm. It is only gonna get worse if court is required. Try and avoid that.