Can not get the shape to cut the way it shows on the screen

I am developing a little box here and I am trying to cut the inside and out side at the same time. I have several different shapes, some set to 0 depth so that the machine should not cut those areas. (using the combine tool is not working properly, in effect it is simply making the two shapes into a combined selection that still cuts the full shape. if that makes sense.)
Can any one help?

Can you share your easel file? I’m not quite clear on what you mean.