Interference of counter propagating beams I am trying to build an optical system where a thin glass plate is illuminated by two mutually coherent beams  E1 and E2 (sketch is below).
My question is: 
Do I get an interference pattern on the glass surface where the two beams overlap?
 
 A: You asked if you will get an interference pattern on the surface of the glass.  Assuming no reflection at the surfaces, the answer is "no" if the two beams are collimated and perpendicular to the glass surfaces, because the phase and amplitude distribution will be uniform along both surfaces.  However, you will get an interference pattern inside the glass consisting of Bragg planes parallel to the glass surfaces.  There will also be an interference pattern consisting of Bragg planes outside the glass in the overlapped counterpropagating beams on both sides of the plate.
Again assuming no reflections, if the glass plate is tilted the plate will be tilted relative to the Bragg planes, and the Bragg planes will intersect the surfaces of the plate.  In this case, there will be an interference pattern on the surfaces, corresponding to the pattern formed by the intersections of Bragg planes with the surface.
When reflections are included, it gets more complicated, because you end up with a lot of beams superimposed and interfering.  
A: Yes, you will observe an interference pattern providing that the reflection effects are small in comparison with penetration ones. For example, when one side of the glass is covered with a photo-sensitive material (photo-plate).
For a true interference at a point $x$ you must have a sum of two different waves at the same time; only then the total intensity will have an interference addenda.
