When assigned oconus, living off base is allowed if a certain percentage of on base housing is occupied, this number varies by location and can change based. Additionally it is possible to get a waiver to live off base even if the on base percentage is not high enough.
On base I believe your partner would not be allowed to live with you unless they were your dependent by a means other than marriage. They would also have to be on your orders, and depending on oconus location there may be additional requirements such as SOFA status, dependent entry approval, a special visa, etc. Could they visit you and stay temporarily? Maybe, probably, who knows.
Speculation, if you lived off base oconus, it would probably be easier for your partner to live with you, assuming they were in the country by some means other than military orders.
