A spin-2 system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins was analyzed by the use of the exact recursion relations in a pairwise approach. The upper layer interacting with nearest-neighbor (NN) bilinear interaction J(1) is laid over the top of the lower layer interacting with bilinear NN interaction J(2), and the two layers are tied together via the bilinear interaction between the vertically aligned adjacent NN spins denoted as J(3). The study of the ground state phase diagrams on the (J(2)/vertical bar J(3)vertical bar, J(1)/vertical bar J(3)vertical bar) plane with J(3) > 0 and J(3) 0 and on the (J(2)/J(1), J(3)/qJ(1)) plane with J(1) > 0 has yielded five distinct ground state configurations. The temperature dependent phase diagrams are obtained for the case with intralayer coupling constants of the two layers with ferromagnetic type J(1) and J(2) > 0, and the interlayer coupling constant of the layers with either ferromagnetic J(3) > 0 or antiferromagnetic type J(3) < 0 on the (kT/J(1), J(3)/J(1)) planes for given values of the J(2)/J(1) for various values of the coordination numbers. As a result, we have found that the model presents both second- and first-order phase transitions, therefore, tricritical points.