Without the second liquid above, the ice displaces a volume of water exactly equal to its own weight. After it melts, the ice becomes the same weight and volume of water, which is why the water level remains constant.
However, the upper liquid layer provides some buoyancy, so less of the ice cube is in the water than if there were no liquid above (i.e. it "sits higher" in the water). Therefore, the ice displaces less water than before but still contains the same amount of water as before, resulting in a rise in the water level after it melts.