Opaque to Transparent animation effect on a textured object (Lerpz)?

I am learning Unity through the great platform tutorial. I've finished it and now trying to improve on it somehow. Currently I am trying to apply a transparency fade-out fade-in effect to the Lerpz (player). However, I've come into many problems as it uses a Bumped Specular shader and not a transparent one.

I have a class which uses the transform.renderer.material.color to modify the alpha channel progressively for a fade-in fade-out effect.

The effect I'm trying to achieve is that Lerpz will slowly fade-out into full transparency and then slowly fade-in to fully opaque mode repeatedly (kind of like a ping-pong effect). (This will be used for an invisibility cloak power).

I've managed to construct a semi-solution for this by changing the material from the script whenever the effect is on to a transparently shaded one. Then used a Lerp based coroutine in C# for a ping-pong alpha cycle. However it only works if I remove the alpha information from the new material texture, but this time some back-side polygons can be seen through the surface and it is really ugly.

So the question: is there a way to smoothly animate between fully opaque and fully trans for a textured object without having problems at the opaque stage?