Ambiguous (and maybe euphemistic) word or phrase for romantic partner

Solution 1:

As discussed in the comments above, companion

This can be a romantic companion, a dinner companion, or a travel companion. It's from the same Latin roots as "company", com panis, "with bread", so at root it's someone with whom you share meals. It's also a term used by couples that feel too aged to be comfortable with boy/girlfriend, and we know from the historical record that the Beasties are always out looking for a female companion

Solution 2:

For use on an ad hoc basis in some situations:

She's only his plus one tonight. I'm not sure they're seeing each other.

Solution 3:

I think you could get away with using partner in crime in a joking manner. It is using "partner" in a manner that would be considered playful if, in fact, the referent considers the relationship romantic. At the same time, someone outside the relationship could only guess apart from non-verbal communication. ("A wink is as good as a nudge.")