Problem with Loop Cuts and Subdivision

I’m modeling an object and when I subdivide or loop cut the bottom or top face, it works normally. However, when I try to subdivide or loop cut the side, front, or back faces, it shows up on the top face. Also, when I subdivide one of the side, front, or back faces, the top is divided into three triangular faces as opposed to four rectangular faces. Does anyone know what’s going on here?
(this object is half of a cube, I’m using the mirror modifier to make it a full size cube and there are only 5 actual faces) q

Actually this is how Subdivide or Loop Cut works - it subdivides Object from “all sides”, not just one face. Also Loop Cut, well, it is a loop and goes in a loop around the Object. So that both things are supposed to appear on different faces as a new edges and verts.
If it stops somewhere, that may be due to so called N-gon - face with more than 4 vertices in the way. This could be the reason why face is divided in triangles.
Switch to Vertices selection mode, select all and check if you do not have some extra left before subdivide or Loopcut. W, Remove doubles and select, X, Dissolve might help to resolve issue.
Post images or blend file on, drop link here.

Welcome on forum!

thanks, you were right, it was an n-gon! I’m fixing the problem right now.