A Monte Carlo investigation of the A thickness (A≡Fe) dependence of the transition and compensation temperatures of a simple cubic Heisenberg A/B bilayer is carried out. Our model, which includes a few mixed planes of the A1−xBx type that represent the disordered interfaces, basically consists of several coupled magnetic parts with different bulk transition temperatures. Numerical results are compared with the experimental data for amorphous Fe/Tb multilayers. The simulated Fe thickness (tFe) dependence of TC, which reproduces the decrease of TC as tFe increases, is consistent with the experimental one. Since our simulations indicate that the magnetic ordering is driven by the disordered interfaces, the decrease of TC is explained by the fact that the interfaces are more and more decoupled as tFe increases. The experimental thermal behavior of each sublattice magnetization can be reproduced with a Tb-magnetic moment of 6μB which seems to be reasonable for amorphous layers, whereas a value of 9μB is too large. Accordingly, a compensation point has been observed for a Fe thickness range that agrees with the experimental one. The simulated and experimental Fe thickness variations of Tcomp are in reasonable agreement.