Character Controller meets Rigidbody

Lately we've been having problems with our Character Controller interacting with physical objects. Example.

In our case the Rigidbody object and the character controller is moving towards each other, which results in the Rigidbody getting pushed back. What we want is for both objects to stop, or for us to have some control in who pushes who. Does anybody know how to achieve this effect?

What we think is happening is that the rigid body is allowed to move too far into the character controller, which then fails it checks and moves inside the object, which is then again pushed back as a fail-safe provided by unity. Any thoughts would be very much appreciated, as it has been a major time-killer.