The setup: Display/shade mode is Textured, Shading is Multitexture
No objects have materials, they're purely textured in the 3D view using the info assigned via UV/Image editor. No objects have "Transparency" checked in the Properties panel/Object/Display pane, but when I've tried it has no effect for this issue.
Question: when selecting objects which are partly or fully overlapped by another object with a texture that is partly transparent, then when one of those objects are selected, the portion that is overlapped by the partially transparent object is entirely masked out.
Is there a way to more appropriately set this up before I get to using the materials? Or can someone point me to a wiki/manual entry for this behaviour if it's the proper behaviour. I've been searching for hours.
Pictures say more than words....
Clear plastic is selected, nothing disappears:

Card backing selected and disappears behind plastic:

Action figure selected, upper body out of plastic, lower body disappears:

Action figure and card backing selected, both disappear behind plastic:

EXTRA UPDATE...
This is very weird. If I grab the set of objects and duplicate and move them, then the viewport rendering weirdness reverses itself: the clear plastic is opaque when unselected; translucent when selected. Further, if I repeatedly select the new created reversed-behaviour objects, duplicate and move, the behaviour reverses again so the clear plastic is translucent, but selecting the character within causes it to be clipped. And so I get something like this:

'Order Independent Transparency' is the buzz-word associated with solutions to this problem. Here is a doc that explains this with images and fancy words. http://on-demand.gputechconf.com/gtc/2014/presentations/S4385-order-independent-transparency-opengl.pdf – MarcClintDion Apr 18 '15 at 08:47