The mixed spin-1 and spin-3/2 Blume-Capel Ising ferromagnetic system (J > 0) with two crystal-field interactions, D-A for spin-1 and D-B for spin-3/2 is studied on the Bethe lattice using the exact recursion equations for the central-spin with spin-3/2. The exact expressions for the order-parameters, the, Curie temperature and the free energy are obtained in terms of the recursion relations. The phase diagrams on the (kT(c)/J, D-A/J) and (kT(c)/J, D-B/J) planes are studied for selected values of D-B/J and D-A/J, respectively, for the coordination numbers q = 3, 4, and 6. Besides the second-order phase transition lines, the lines of the first-order phase transitions terminating either at a tricritical point or at an isolated critical point are found. The thermal variations of the order-parameters are studied with two formulations, both obtained on the Bethe lattice for the mixed spin-1 and spin-3/2 Ising system using the exact recursion relations, but one with the central-spin with spin-1 and the other is for the central-spin with spin-3/2 for q = 3, thus, it is shown that the choice of the central-spin on the Bethe lattice has no effect on the phase diagrams. (C) 2003 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.