The quenched decorated Ising model with competitive interactions recently introduced by Fittipaldi et al.1 is herein extended to the Heisenberg case. The model consists of planes in which the nodal spins interact antiferromagnetically (J<0) with their nearest neighbors, and ferromagnetically (K>0) with the spins that decorate the bonds, which are quenched randomly distributed over the lattice. The planes, which simulate the CuO2 layers in doped cuprates superconducting materials, interact antiferromagnetically (J′=λJ). By using the framework of an effective-field theory with correlations, we discuss the 3D antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T−p), for various values of both interplane and intraplane exchange parameters λ and α=|J|/K, respectively. In particular, our numerical estimates of the vanishing temperature critical concentrations pc [i.e., pc at which TN(pc)=0] well compare with the experimental data of Kitaoka et al.2 for the La2−xBaxCuO4 in the nonsuperconducting phase.