When a chest, ender chest, boat or bed is placed behind dropped Stained Glass or Stained Glass Pane it is not shown, it's transparent. See attached images.
I also tried with the following blocks, which did show up properly behind Stained Glass, if that helps debugging the issue.
Powered Rail, dispenser, oak leaves, trapdoor, oak fence.
I did the testing in a singleplayer world, superflat with cheats allowed and originally found it while playing on version 1.8.8, so it is not exactly something new.