  The Pair Approximation method is applied to the antiferromagnetic
Heisenberg-Ising spin-1/2 bilayer with a simple cubic crystalline structure.
The method allows for self-consistent calculations of thermodynamic quantities,
based on the determination of Gibbs free-energy. In the paper the phase
diagrams and planar magnetizations are calculated for the system in question.
Special attention is paid to the case of magnetically non-equivalent planes,
one of which is additionally randomly diluted. The occurrence of a compensation
phenomenon is found and the compensation temperature is discussed for such a
system. The characteristic concentration of magnetic atoms $p^{\star}$, below
which the compensation phenomenon vanishes, is examined as a function of the
Hamiltonian parameters.
