Transparency and Materials

I have a plane gameObject that I added a material to, then selected a color for that material. I want to put a border around the plane that is a lighter color than the color of the rest of the plane. I figured the easiest way to do this, since I would be doing this for several different colored planes, was to overlay an image with white semi-transparency to lighten the colors around the edges. I created the image below:

If you can't see it, this is a box with a transparent center and a semi-transparent white border. When I applied this image as my texture, the effect was not as I intended. As a diffuse material, nothing is transparent. As a transparent/diffuse material, the center of the square appears entriely transparent. Does anyone know how to make this work?