  The exploration of cold polar molecules in different geometries is a rapidly
developing experimental and theoretical pursuit. Recently, the implementation
of optical lattices has enabled confinement in stacks of planes, the number of
which is also controllable. Here we consider the bound state structure of two
polar molecules confined in two adjacent planes as function of the polarization
angle of the dipole moment of the molecules. We prove analytically and present
numerical evidence for the existence of bound states for arbitrary dipole
moments and polarization directions in this two-dimensional geometry. The
spatial structure of the bound states is dominated by two-dimensional s- and
p-waves, where the latter exceeds 40 percent over a large range of polarization
angles for intermediate or strong dipole strength. Finally, we consider the
influence of the dimer bound states on the potential many-body ground-state of
the system.
