Mouse events for object with character controller

I am trying to use OnMouseEnter and OnMouseExit in a script attached to an object with a character controller. This doesn't appear to work. I cannot add a collider to the object without losing the character controller, which I need on the object. I tried adding a box collider to a child of the object, but that didn't work either. Does anyone know of a workaround to make this work? Any help is greatly appreciated. -Larry