I concur with britsimon that if you or your husband were in the UK for over 12 months then you will require a police certificate from there (I also had to get one from the UK as I lived there for 5 years).
The UK police certificate doesn't take long (maximum two weeks) however there are a few catches as follows:
- You will need a lawyer (or one of the qualified persons stated in the application form) to sign your photographs and forms.
- ACRO (Association of Police Officers Criminal Records Office) does not courier certificates. They either do international post which may take time and also they do not post to P.O. Box addresses for security reasons.
- You will need to pay the correct fee in Great British Pounds

and it should be from a UK bank account/cheque.
- You will need evidence of proof of address in the form of utility bills or any similar documentation (bank statement showing your address will do as well).
Those are the key items but check the ACRO site because the forms and instructions are all there for immigrant to USA police certificates.
The Australian police certificate isn't necessary as you've not been there for more than 12 months but you can take it anyway if you wish to.
Case No - DV2013AF0007XXXX (applied the first time and got it the first time - lucky me!)
Entry Checked - 1st May 2012
Forms Sent To KCC - 10th May 2012
Received By KCC - 12th May 2012
Confirmation From KCC - 25th May 2012 after I sent them an email
2nd NL - 14th June 2013
Police Clearance (TZ) - 13th June 2013
Police Clearance (UK) - 21st June 2013
Medicals - Completed 24th June 2013
I-134 - 16th July 2013
Bank Statements - 22nd July 2013
Interview - Wednesday, August 7th 2013 @ 8am - US Embassy Tanzania
Visa Pick up - Hopefully August 11th 2013
Departure Date - August 17th 2013
Port of Entry - Washington Dulles