2 inches is a LOT. I would probably go 1/4" foam with a fiberglass skin on each side. Note that the foam needs to be very stiff - even brittle. Regular insulating foam probably does not have the most desireable strength features and would be too flexible to provide proper structure as the center of a composite lamination.

In a sandwich construction like this, the foam performs a similar function as the webbing in an "I" beam. You can think of it like this - Fiberglass is strongest when it is in tension ... i.e. being pulled. Like most materials, it's not very strong when being pushed together from it's ends (compression). If you have a sandwich construction, and try to bend the assembly, the inner fiberglass layer is in compression where it is unable to resist very well. However, the foam helps transfer this loading to the outer skin and because of the sandwich arrangement, the outer skin is in tension - it's strongest point. The outer skin will support the entire assembly. If you bend it in the opposite direction, the loading on the skins is opposite and the unit is stiff in both directions.

The properties of the foam are important for this transfer of stress to occur properly. The foam's duty is to handle a good bit of shear stress as it prevents the two skins of fiberglass from sliding in relation to each other. If they slide, the tension of one side is no longer supporting the compression of the other and the compression side will buckle leading to failure of the entire thing. In order to adequately handle this shear, the foam needs to be stiff...and waterproof to keep from getting soggy.