The Pair Approximation method is applied to studies of the magnetic Ising-Heisenberg bilayer with simple cubic structure and spin S = 1/2. The method allows to take into account quantum effects related to Heisenberg couplings. In the paper the entropy and magnetic contribution to the specific heat are calculated. A special attention is paid to the case when the planes are magnetically non-equivalent and the interplanar coupling is relatively weak. A double peak structure in the temperature dependence of the specific heat and the entropy change in the external field is found. When the system is strongly anisotropic (the case of Ising couplings) the Exact Calculations for Finite Clusters are performed for comparison with the Pair Approximation method. (C) 2013 Elsevier B.V. All rights reserved.