  We propose and study a model of polymer chains in a bilayer. Each chain is
confined in one of the layers and polymer bonds on first neighbor edges in
different layers interact. We also define and comment results for a model with
interactions between monomers on first neighbor sites of different layers. The
thermodynamic properties of the model are studied in the grand-canonical
formalism and both layers are considered to be Cayley trees. In the core region
of the trees, which we may call a bilayer Bethe lattice, we find a very rich
phase diagram in the parameter space defined by the two activities of monomers
and the Boltzmann factor associated to the interlayer interaction between bonds
or monomers. Beside critical and coexistence surfaces, there are tricritical,
bicritical and critical endpoint lines, as well as higher order multicritical
points.
