  We study the phase diagram of fermionic polar molecules in a bilayer system,
with an imbalance of molecular densities of the layers. For the imbalance
exceeding a critical value the system undergoes a transition from the uniform
interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with
a stripe structure, and at sufficiently large imbalance a transition from the
FFLO to normal phase. Compared to the case of contact interactions, the FFLO
regime is enhanced by the long-range character of the interlayer dipolar
interaction, which can combine the s-wave and p-wave pairing in the order
parameter.
