I've had this problem too. It seems like the normals are flipped,
or that there is some weird alpha chanel thing going on,
but it still happens even when I save the.bmp files as 24bit.
I never have figured out why this happens, but I do know how to fix it.

First save the .bmp you are using in Max to a .pcx file. You can't
use .pcx images as a diffuse map in Max, so you'll just need 2 versions
of the image.

Once you have exported the model, open it in MED, select File->Skin Editor.
From the Skin Editor select File->Import->Skin Image. Browse to the
.pcx file to load it. Save the model and it should look right when you
run it in the engine.