[en] We study a two-dimensional (2D) spin-half Heisenberg model related to the quasi-2D antiferromagnets (Ba, Sr)₂Cu₃O₄Cl₂ by means of exact diagonalization and spin-wave theory. The model consists of two inequivalent interpenetrating square-lattice Heisenberg antiferromagnets A and B. While the antiferromagnetic interaction J_AA within the A subsystem is strong the coupling J_BB within the B subsystem is much weaker. The coupling J_AB between A and B subsystems is competing, giving rise to interesting frustration effects. In dependence of the strength of J_AB we find a collinear Neel phase, non-collinear states with zero magnetizations as well as canted and collinear ferrimagnetic phases with non-zero magnetizations. For not too large values of frustration J_AB, which correspond to the situation in (Ba, Sr)₂Cu₃O₄Cl₂, we have Neel ordering in both subsystems A and B. In the classical limit these two Neel states are decoupled. Quantum fluctuations lead to a fluctuational coupling between both subsystems ('order from disorder') and select the collinear structure. For stronger J_AB we find evidence for a novel spin state with coexisting Neel ordering in the A subsystem and disorder in the B subsystem