Gaussian DoF on translucent material

Nick, thank you for explanation!

So what will be your suggestion to make scene for 2D platform game that use textures with alpha? What material should I use to have proper alpha from textures and depth of field? One of the textures that I use is here:

I can pre-blur texture in Photoshop, but that will be tricky to get proper DoF on each scene where I need about 5 layers in parallax (as background). So is there a way, how add blur effect to specific translucent material and change amount of it in realtime?

Thank you!