I recently added an inside set of doors into my CTF level.
But as you can see from the video it looks fine. Until you back away. Then you start to get Z fighting.
I tried making the interior door thinner, but it would have been too thin.
I will add this kind of door in another level, but instead of putting it inside of another door mesh, I will make the door from 3 seperate sections. 2 outer doors and one inner set of doors.
Watch the video on youtube to see a full screen 720 version of it.