  We propose a two-dimensional model for a multilayer stack of dipolar
Bose-Einstein condensates formed by a strong optical lattice. We derive
effective intra- and interlayer dipole-dipole interaction potentials and
provide simple analytical approximations for a given number of lattice sites at
arbitrary polarization. We find that the interlayer dipole-dipole interaction
changes the transverse aspect ratio of the ground state in the central layers
depending on its polarization and the number of lattice sites. The changing
aspect ratio should be observable in time of flight images. Furthermore, we
show that the interlayer dipole-dipole interaction reduces the excitation
energy of local perturbations, affecting the development of a roton minimum.
