A bilayer Ising model consisting of two Bethe lattices each with a branching ratio of q Ising spins with one of the layers having only spin-1 atoms and the other having only spin-3/2 is laid over the top of the other and the two layers are tied together via an interaction 2 between the vertically aligned spins. Besides, the obtaining of the ground state (GS) phase diagrams on different possible planes depending on the given system parameters, the variations of the order-parameters and the free energy are investigated by the use of the exact recursion relations in a pairwise approach to obtain the temperature dependent phase diagrams of the model by considering only the ferromagnetic ordering in each of the layers and ferromagnetic or antiferromagnetic ordering of the adjacent nearest-neighbor (NN) spins of the layers. It was found that the system presents both second- and first-order phase transitions. The lines of the first-order phase transitions are found to end at the isolated critical points. The model also presents compensation temperatures when the bilinear interaction of the upper layer with spin-1 can compete with that of the lower layer's with spin-3/2. (C) 2007 Elsevier B.V. All rights reserved.