  Supersolid phases as a result of a coexistence of superfluid and density
ordered checkerboard phases are predicted to appear in ultracold Fermi
molecules confined in a bilayer array of two-dimensional square optical
lattices. We demonstrate the existence of these phases within the inhomogeneous
mean-field approach. In particular, we show that tuning the interlayer
separation distance at a fixed value of the chemical potential produces
different fractions of superfluid, density ordered, and supersolid phases.
