I just also did this 3D simulation on a top layer differential micro-strip lines, hence there is no ambiguity about the reference plane, and still it gives ~135 ohm differential impedance. The HyperLynx 2D solver gives ~108 ohm differential impedance. Now I think something is wrong with IE3D while simulating a very simple transmission line.
from what you wrote it is hard to say why there is such big difference. It would require to have a look at what you extracted to HL3D.
Regarding the usage of multiple reference layers it is possible to use both (upper and lower) layer in the simulation. During port setup just assign the positive port to the trace, then the negative layer to the lower layer and directly after this another negative port to the upper layer. Should finally look like the screenshot below.