Rigidbody2D ignores Character Controller

I have the following case in Unity 5.2.3f1:

1. Stone (Rigidbody2D + BoxCollider2D) is flying;

2. P1 (CharacterController only) is standing;

3. Stone has the script onHit.cs, which implements:
   void OnCollisionEnter2D (Collision2D coll) {Debug.Log("Stone hits something!");}
void OnCollisionStay2D (Collision2D coll) {Debug.Log("Stone is hitting something!");}

4. Stone hits P1 in the head, coming from above, and continues falling across it;

5. No message displayed.

I have no idea what is going on and why the collision isn't triggered. I have read something about void OnControllerColliderHit(ControllerColliderHit hit), but it isn't triggered either, since P1 is not moving (and I REALLY need the Stone to react to a collision with an idling player). My goal is to affect the Stone's velocity ONLY, and that is why I think I should not use void OnControllerColliderHit(ControllerColliderHit hit) in this case (am I wrong)?