  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 JAA within the A subsystem is strong the coupling JBB within the B
subsystem is much weaker. The coupling JAB between A and B subsystems is
competing giving rise for interesting frustration effects. In dependence of the
strength of JAB 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 JAB, which
correpond 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 JAB we
find evidence for a novel spin state with coexisting Neel ordering in the A
subsystem and disorder in the B subsystem.
