We study Hartree-Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x- and y-directions and a possibly different hopping parameter t(z) in the z-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases t(z )= 0 and t(z )= t, respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that t = 1, we analyze how the Neel temperature and the antiferromagnetic mean field depend on the coupling parameter, U, and on the hopping parameter t(z). We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as t(z )-> 0. It is found that the asymptotic formulas are qualitatively different for t(z )= 0 (the two-dimensional case) and t(z )> 0 (the case of nonzero hopping in the z-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit t(z )-> 0 in which the three-dimensional model reduces to the two-dimensional model.