Texture+non-texture transparency/blend problem

I’d appreciate any help with this one issue with my hair system.

My goal is to have transparency on hair so the edjes will look ragged, showing sheaths of hair strands, etc., which will appear to be free-floating.

I made nearly half of the hair transparent to help troubleshoot:

You can see that texture/texture transparency is working perfectly.  You can see through the transparent part of the hair image to the inside of the hair image to the left and also to the eyeball image.  The problem is, the transparency only holds for other textures on the other side.  If there is no texture on the other side (like plain world background, or the psychedelic sphere here), it shows black.

I have my Blend state on the root node, and I have updated the render state.  I have tried 1-side and 2-sided.  It’s not a spatial relationship issue, because I have put a psychedlic sphere and the eyes as peers and the problem is still the same.  I’ll try some other texture combine modes, but I’m not hopeful, since the problem is not with texture/texture blending, it’s with texture/non-texture.

Fixed, thanks to Ashton.

I was missing the TestFunction in my blend state setup.  Long ago when I copied that code, I somehow stupidly thought that this "test" had to do with test mode or something, not test as in evaluate/compare.  I did try it at the time and it seemed to have no effect (at that time I obviously didn't have items in my scene which needed to combine in this way).