Check with your Post Office. My USPS Post Office Box actually has a street address I can use, as well. They started this about four or five years ago. It's the street address of the Post Office, with the box number added like an apartment number. (Interestingly, the Zip+four is different.)
Therefore you can list the "box" as a "unit" number, or "ste" (suite) or "apt" (apartment). Ask the 3rd party service prior to contracting.
I had such a service in NYC (they're common, lotsa businesses love having a Suite address on 5th Ave, or whatever).
I'd test it before committing to a long term contract though.