I carry the ins for my family. The questioned asked: What type of HDHP did my spouse have on 12/1/16? Does it mean if it was thru his employer? He doesn't work.

None is the correct answer.  You are reasoning correctly: the question is asking if he has his own HDHP.  Since he is covered by your Family HDHP, he does not have an HDHP of his own.  So you should just say "none" in that box, and it should remove that diagnostic.