  Motivated by the geometry of spins in the material CaCu$_2$O$_3$, we study a
two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings
J and \alpha*J along the two axes in the plane and a coupling J_\perp
perpendicular to the planes. We study these class of models using the
Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite
temperatures and series expansion methods at T=0. The critical value of the
interlayer coupling, J_\perp^c, separating the N{\'e}el ordered and disordered
ground states, is found to follow very closely a square root dependence on
$\alpha$. Both T=0 and finite-temperature properties of the model are
presented.
