Try this web site which is US oriented but the info applies equally to Australians:-
http://www.italiamerica.org/
On the right hand side is a link titled "Information for Italian Dual Citizenship"
There is no such thing as a "European passport". Individual European Union countries issue passports in a uniform style, (dark red cover etc) which may have confused you.
I would guess your best chance would be to apply for Italian/Australian dual citizenship.
Italian Citizenship from: MOTHER
Mother:
Your mother was an Italian citizen at the time of your birth
NOTE: "Italian citizen at the time of birth" means that he/she did not acquire any other citizenship through naturalization, before the descendant's birth.
You were born after January 1st, 1948
You never renounced your right to Italian citizenship.
If citizenship is acquired by birth in your country and you meet all these conditions, you qualify for Italian citizenship jure sanguinis. You must obtain certified copies of the following documents:
Your mother's birth certificate from Italy.
Your father's birth certificate
Your parents' marriage certificate (If married outside of Italy, you will need an apostille and a translation into Italian.)
Your parents' divorce decree/certificate, if applicable (with apostille and translation)
Your mother's certificate of naturalization OR Italian passport and permanent resident card/green card.
Your birth certificate (with apostille and translation)
Your mother's death certificate, if applicable (with apostille and translation)
Your father's death certificate, if applicable
Your marriage certificate, if applicable (with apostille and translation)
Your divorce decree/certificate, if applicable (with apostille and translation)
Your spouse's birth certificate, if applicable
Birth certificates for all your children under the age of eighteen, if applicable (with apostille and translation)