How do I make a block "cutout" but also not have transparent parts?

Alright, so I'm making side slabs, and when I set the transparency type to "cutout," it automatically forces the "block has transparent parts" checkbox to be checked, and I think this might be causing an issue with the side slabs:

Whenever a full block or regular slab is placed on the side that would produce a gap between the side slab and the other block, the face facing the other block becomes transparent.

Is there a way to fix this?

EDIT: I should probably also mention that the same thing happens when I have the slabs set to "solid."