Maybe this will help illustrate better.  I don't think it actually is in need
of 'inverse' anywhere upon checking it out more.

light_source { <10,10,-10> color rgb 1}
camera {
  location  <0,0,-5>
  angle 40
  look_at   <0,0,0>
}
background {rgb<1,1,1>}

difference { // plane slicing
difference { // merge used here leaves both globes
difference { // globe_1
sphere {0,1} sphere {0,.9}
}
difference { // globe_2
sphere {0,1} sphere {0,.9}
 scale <1,1.25,1> translate .5*y
}
}
 plane {z,0}
 pigment {rgbf<1,0,0,.5>}
 finish {specular .5}
}

This will do what you wanted I think.  I'm not sure what you were seeing
yourself.  'merge' will leave both globes behind though so maybe that was why
you thought it was solid.  Maybe...

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