  The mean-field and effective-field approximations are applied in the study of
magnetic and thermodynamic properties of a spin-$1/2$ Ising system containing
three layers, each of which is composed exclusively of one out of two possible
types of atoms, \textbf{A} or \textbf{B}. The \textbf{A-A} and \textbf{B-B}
bonds are ferromagnetic while the \textbf{A-B} bonds are antiferromagnetic. The
occurrence of a compensation phenomenon is verified and the compensation and
critical temperatures are obtained as functions of the Hamiltonian parameters.
We present phase diagrams dividing the parameter space in regions where the
compensation phenomenon is present or absent and a detailed discussion about
the influence of each parameter on the overall behavior of the system is made.
