It's how the alpha's overlap that cause the one wiremesh not to be visible when looking at it through the other.
Right click on the NiAlphaProperty and try out these settings: http://i647.photobucket.com/albums/uu195/mark507_album/stuff/Untitled-2.png
I suggest tweaking the 'Alpha Test Threshold' value to whatever looks best.
Using settings similar to these is a well known method of stopping alphas from overlapping wierdly, but it doesn't seem to work well with alphas which use alpha gradients, however for what you want this shouldn't matter.
I suggest learning Blender if you have the time, and don't have access to a later version of 3ds max, as max 4 and 5 are only really good for particles, and if you're not interested in these, Blender with it's newer functions, easier methods, and vast array of tutorials should serve you better.