What is the most natural way to disambiguate "with"?
Solution 1:
You can disambiguate the first sense by saying "in" instead of "with".
I'm an officer in the NYPD.
I'm not sure if there's a universal way to disambiguate the 2nd case, but there may be specific terms appropriate to different situations. For example,
a reporter embedded with the Army Rangers
or
a British soldier seconded to the US Air Force
or
a groupie following Kanye West
but the appropriate terms will depend on the specific circumstance.