  We present a spin-rotation-invariant Green-function theory for the dynamic
spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a
stacked honeycomb lattice. Employing a generalized mean-field approximation for
arbitrary temperatures, the thermodynamic quantities (two-spin correlation
functions, internal energy, magnetic susceptibility, staggered magnetization,
N'eel temperature, correlation length) and the spin-excitation spectrum are
calculated by solving a coupled system of self-consistency equations for the
correlation functions. The temperature dependence of the magnetic (uniform
static) susceptibility is ascribed to antiferromagnetic short-range order. The
N\'{e}el temperature is calculated for arbitrary interlayer couplings. Our
results are in a good agreement with numerical computations for finite clusters
and with available experimental data on the \beta-Cu2V2O2 compound.
