Dani - did you get married in the US or in Aus, and how long have you been married? If you still have your Aussie citizenship, your hubby would have to apply for a Spouse VISA. You will need to provide proof of your relationship - cards you've sent each other, correspondence addressed to both of you, lease/mortgage/utility bills in both your names, etc.
In some cases this type of VISA can be a two-stage process - temporary residency followed by permanent residency after two years, followed by citizenship after another two years.
If you have been married for more than 5 years, or if you have been married for more than 2 years and have children together who are still dependent on you, then it is likely that the temporary requirement will be waived and a permanent VISA granted from the start.
Under both temporary and permanent spouse VISAs, your husband would be entitled to seek permanent employment and claim Medicare benefits.
This link will give you more information:
http://www.immi.gov.au/migrants/partners/spouse/309-100/index.htm
