As long as you have an active duty identification card and orders or leave papers then by courtesy you should be admitted. I have seen several foreign military in uniform in various USOs. Your dependents should also be welcome. You might want to call ahead and get the name of the supervisor you speak to just in case. Most personnel at the USO are volunteers. Many many times I have been there and the only people there were new and didn't know all the rules.
You may have access if you have your Australian Military ID must be active though. I know USO is not affiliated directly with the Pentagon who are the ones who grant access to our Allies to our bases but USO may grant access along the same guidelines
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