If I understand correctly, the problem is that you are trying to give 3-D properties to a 2-D element type. 2-D orthrotropic element types will not consider the out of plane compression and, therefore, is not concerned with E3.
OK, time to "knock some cobwebs loose". You have to define your element type as "Laminate". You set up two different materials: one for your aluminum skins and one for your core. Your aluminum skins can be 2-D orthotropic, but your core would need to be 3-D orthotropic, not 2-D. When you define the layers in your laminate, select material 1 for the first skin, give it a thickness...you may even be able to use isotropic material properties for this...I haven't really tried it this way. For the second layer input into the laminate, select material 2, give it a thickness. Then for the third layer in your laminate, select material 1 again to provide for the other skin. My only concern is whether you can apply a 3-D orthotropic material to a 2-D representation. I have to admit that I'm not sure how the processor will handle this.
Garland E. Borowski, PE