What works for me is to have two large rectangle containers in the cabinet (like plastic bins with out the lids). The containers stack in one (or are tossed randomly)and the lids go in the other (stacked sideways by height).
So to find what you want you pull out the large box of containers, then quickly pull out the large box of lids and grab the appropriate one. Then shove the whole thing back in the cabinet.
At least you won't be searching through the whole cabinet this way looking for a lid and your dear husband can still toss them in (just make sure he hits the holding bin).
P.S. Another idea is to start over with all new containers like that ones on t.v. infomercials (I think they also sell it at Bed, Bath and Beyond) that all stack with their lids on a "lazy susan" type thing.