Prevent character controller from moving along certain axis.

My character uses mecanim root motion to move itself and a character controller for collision.

What im trying to do is to prevent the character controller from moving along the Z axis. I know that this can be done with rigidbodies, But my character script depends on the character controller, And when i tired using mecanim root motion with a rigidbody, the player had difficulties moving and changing directions.

Can anyone provide me an example in C# (if this is possible)?