The two-layer spin-1 Ising model on the Bethe lattice is studied in terms of the intralayer coupling constants J(1) and J(2) of the two layers, interlayer coupling constant J(3) between the layers and the external magnetic fields, which are coupled to the two layers and assumed to be different for each layer, for given values of the coordination number q by using the recursion relation scheme. The ground-state configurations of the system are obtained on the (J(2)/vertical bar J(1)vertical bar,J(3)/q vertical bar J(1)vertical bar) planes depending on J(1) < 0 or J(1) > 0. Then, the phase diagram of the system is obtained on the (kT/J(1),J(3),J(1)) plane for given values of alpha = J(2)/J(1), and q in zero external magnetic fields. It was found that the system presents both first- and second-order phase transitions for all values of q. Besides, we also present the thermal change of the total and staggered magnetizations of the two layers and also the spin-spin correlation function between the nearest-neighbor spins of the adjacent layers. (c) 2006 Elsevier B.V. All rights reserved.