Also, you as an Australian citizen would be able to claim all benefits anyway, it would be your husband that may not be able to claim certain benefits.
This is not exactly true, as the partner's status determines how much the Australian partner can claim and also how much will be deducted from her payment when she earns income through work.
Obviously she can only claim at the reduced partnered rate, but in addition to this the amount you can earn before your payment is reduced - and by how much - is very different if you fall under the category 'Partner doesn't get a Centrelink pension', even if they have no income.
See
https://www.humanservices.gov.au/individuals/enablers/income-and-assets-tests-parenting-payment
eg. if the Australian partner receives Parenting Payment and her partner IS receiving a Centrelink pension, then on top of the double pension, the couple only lose 25c then 30c in the dollar for every dollar earnt above $208 / $508 per fortnight.
If the foreign partner is ineligible and thus NOT receiving a Centrelink pension (and has no work), then even if the Australian partner works, the family will lose 50c then 60c in the dollar for every dollar she earns over $104 / $254 per fortnight.
This makes it really hard for the Australian partner working part time (for instance mothers of young children) to support a partner who hasn't found work, as they are only better off to the tune of 40% of any income earned, up until they earn $953 a fortnight, at which point the parenting payment drops out altogether.