Do OnMouse functions work on child colliders?

I'm in the initial stages of setting up some button functionality for my game and was planning on using the following structure:

• Have an empty game object called "Interface Controller" and attach an InterfaceController script

• Add a child game object with a collider for every button

• Using OnMouseDown in the InterfaceController script, check the tag of the collider object to perform button action

However, the OnMouseDown function is not triggering for the child object colliders. I'm using a really simply script to test:

     void OnMouseUpAsButton()
     {
         Debug.Log("Clicked!");
     }

It will work when I attach the script to the child object, but not the parent. It seems really messy to have the same script or a unique script attached to every button. Is there any way I can do this from the parent?