I'm guessing that a non-spouse dependent has a dep_relation code of A, D, F, G, S, or X. Based on that, I would do this:
SELECT [fields]
FROM (partfile INNER JOIN depfile AS Spouse ON partfile.prt_ss_nbr = Spouse.dep_ss_nbr AND Spouse.dep_relation = [Spouse code])
WHERE partfile.prt_ss_nbr NOT...