The magnetic properties of the ternary system ABC consisting of spins sigma = 1/2, S = 1, and m = 3/2 are investigated on the Bethe lattice by using the exact recursion relations. We consider both ferromagnetic and antiferromagnetic exchange interactions. The exact expressions for magnetizations and magnetic susceptibilities are found, and thermal behaviors of magnetizations and susceptibilities are studied. We construct the phase diagrams and find that the system exhibits one, two or even three compensation temperatures depending on the values of the interaction parameters in the Hamiltonian. Moreover, the system undergoes a second-order phase transition for the coordination number q <= 3 and a second- and first-order phase transitions for q>3; hence the system gives a tricritical point. The system also exhibits the reentrant behaviors. (C) 2008 Elsevier B.V. All rights reserved.