Using Padding and Margins with Graphics object

I think adding another frame will do what you want. Like so:

Manipulate[
  Framed[
    Framed[
      GraphicsGrid[
        {{Graphics3D[Background -> Green, ImagePadding -> 20], 
          Graphics3D[Background -> Yellow, ImagePadding -> 0]}},
         Background -> LightGray,
         ImageSize -> {400, 200},
         Frame -> True],
      FrameStyle -> None,
      Background -> Red,
      FrameMargins -> {{a, a}, {b, b}}],
    FrameStyle -> {Red, AbsoluteThickness[2]},
    FrameMargins -> 30,
    Background -> White],
  {{a, 20}, 0, 20, 1, Appearance -> "Labeled"},
  {{b, 20}, 0, 20, 1, Appearance -> "Labeled"}]

You can use Show to modify the background of the Graphics expression returned by GraphicsGrid:

Manipulate[
 Framed[
  Show[
   GraphicsGrid[
    {{Graphics3D[Background -> Green, ImagePadding -> 20], 
      Graphics3D[Background -> Yellow, ImagePadding -> 0]}},
    Background -> LightGray,
    ImageSize -> {400, 200}, Frame -> True, 
    PlotRangePadding -> {a, b}
    ],
   Background -> Red
   ],
  FrameStyle -> Red, FrameMargins -> 30, Background -> White
  ],
 {{a, 20}, 0, 20, 1, Appearance -> "Labeled"},
 {{b, 20}, 0, 20, 1, Appearance -> "Labeled"}
 ]

This works because GraphicsGrid returns a Graphics expression with the contents placed as Inset. The Background specified in the options to GraphicsGrid is implemented using Rectangle directives, since it needs to be flexible enough to support coloring of individual grid cells, which also explains why the PlotRangePadding is added "around" the background.