haha I am thinking Medford or Klammath Falls

Opposite sides can see the moon simultaneously. It will be for a shorter period, but for all two points on the earth there should be at least a single time per moon orbit that the moon is visible by both at the same instant.

The moon is reversed if the other person is seeing it on the other side of the planet, so technically not the same moon face.

Clarification:

I did not mean the dark side, we can't see that. I meant the orientation. Like this:

Some goes with east and west.