Well, that's something they weren't able to solve when they invented all this hardware accelerated graphics business and sounds like we'll have to deal with this for a long while.
The issue here is that graphic cards do not sort the polygons, nor objects. The graphics card is "dumb", you tell it to draw an object and it will draw the pixels that represent it and also, in another non-visible "image" called zbuffer (or depthbuffer), will draw the pixels that represent the object but instead of color it will draw the distance to the camera for each pixels. Any other objects that you draw afterwards, the graphics card will check if the distance to the camera for each pixel, and if it's farther, it won't draw it (unless you disable the check, that is).
This speeds up things a lot and gives you nice intersections between solid objects. But it doesn't play well with transparency. Say that you have 2 transparent objects and you want A to be drawn behind B. You'll need to tell the graphics card to draw A first and then B. This works fine as long as they're not intersecting. In order to draw 2 transparent objects intersecting then the graphics would have to sort all the polygons, and as the graphics card doesn't do that, then you'll have to do it.
It's one of these things that you need to understand and specifically tweak for your case.
In three.js, if you set material.transparent = true
we'll sort that object so it's drawn before (earlier) other objects that are in front. But we can't really help you if you want to intersect them.