The critical and the compensation temperatures of the mixed spin-3/2 and spin-2 Ising ferrimagnetic system is examined on the Bethe lattice by using the exact recursion equations. First, the ground state phase diagram of the system at zero temperature is obtained on the (DA/q vertical bar J vertical bar, D-B/q vertical bar J vertical bar) plane. Then in order to investigate the influences of the sublattice crystal fields at higher temperatures, the phase diagrams on the (kT vertical bar J vertical bar, D-A/vertical bar J vertical bar) and (kT/vertical bar J vertical bar, D-B/vertical bar J vertical bar) planes are-calculated for given values of D-B/vertical bar J vertical bar for spin-2 and D-A/vertical bar J vertical bar for spin-3/2 respectively. Besides the second-order phase transition lines, two types of the first-order lines one ending at a tricritical point and the other at an isolated critical point are found. The model also exhibits up to four compensation temperatures for appropriate values of the system parameters. The calculations are carried out for the coordination number q = 3 corresponding to the honeycomb lattice. (c) 2006 Elsevier B.V. All rights reserved.