  We propose a model for addressing the superfluidity of two different Fermi
species confined in a bilayer geometry of square optical lattices. The fermions
are assumed to be molecules with interlayer s-wave interactions, whose dipole
moments are oriented perpendicularly to the layers. Using functional integral
techniques we investigate the BCS-like state induced in the bilayer at finite
temperatures. In particular, we determine the critical temperature as a
function of the coupling strength between molecules in different layers and of
the interlayer spacing. By means of Ginzburg-Landau theory we calculate the
superfluid density. We also study the dimerized BEC phase through the
Berezinskii-Kosterlitz-Thouless transition, where the effective mass leads to
identify the crossover from BCS to BEC regimes. The possibility of tuning the
effective mass as a direct consequence of the lattice confinement, allows us to
suggest a range of values of the interlayer spacing, which would enable
observing this superfluidity within current experimental conditions.
