I am pretty sure that there are some gliders which have the wings filled with foam, but the strength is in the skin over the foam! I wonder about the "Goodyear" blimp and if it has any internal bracing?
The foam core is designed to carry the shear stresses and transfer them into the bonded skin (usually glass/polyester or graphite/epoxy). And because they're continuously bonded, the foam stabilizes the skins, so skin stability (compressive and/or shear buckling) is not an issue. In addition, bonded structures are typically very stiff, and don't suffer from the flexibility and high local stresses that mechanically fastened joints can have. So actually the skins AND the foam core are both crucial to the strength AND stiffness.
Blimps have a lightweight internal structure that is mainly there to transfer local loads (gondola attachments or say the mooring tower attachment at the nose) into the envelope. It's nothing like the far more substantial structure of a dirigible.