The critical and compensation temperatures of the bilayer Bethe lattices with one of the layers having only spin-1/2 atoms and the other having only spin-1 atoms placed symmetrically are studied by using exact recursion relations in a pairwise approach. The Hamiltonian of the model consist of the bilinear intralayer coupling constants of the two layers J (1) and J (2) for the interactions of the atoms in layers with spin-1/2 and spin-1, respectively, and the bilinear interlayer coupling constant J (3) between the adjacent atoms with spin-1/2 and spin-1 of the layers. After obtaining the ground state phase diagram with J (1) > 0, the variations of the order-parameters and the free energy are investigated to obtain the phase diagram of the model by considering only the ferromagnetic ordering of the layers, i.e. J (1) > 0 and J (2) > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent spins of the layers, J (3) > 0 or J (3) < 0, respectively. It was found that the system presents both second- and first-order phase transitions and, tricritical points. The compensation temperatures was also observed for the appropriate values of the system parameters.