Hi rickles,
for model aircraft I've used UHU Por for many years on depron ( which is foamboard without a card facing) and it is the standard adhesive in aeromodelling circles, though it is best to avoid excess glue outside of the joint as it does not 'sand' well and can be pulled out of the joint.
A good adhesive to use is epoxy both fast and slow types are okay and will not dissolve the foam and produce a firmer joint. You can also use PVA to glue wooden parts to the card facing. Another foam safe adhesive ,but really only suitable for low strength joints is Copydex.
Trevor