The spin-3/2 Ising model is investigated for the case of antiferromagnetic (AFM/AFM) interactions on the twolayer Bethe lattice by using the exact recursion relations in the pairwise approach for given coordination numbers q = 3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state (GS) phase diagrams are obtained on the different planes in detail and then the temperature-dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q, therefore, tricritical points. It is also found that the system exhibits double-critical end points and isolated points. The model also presents two Neel temperatures, T(N), and the existence of which leads to the reentrant behaviour.