The preparation, X-ray crystal structure, and optical and magnetic properties of a polymeric two-dimensional mu-2,2’-bipyrimidine (C8H6N4, bpym), mu-oxalato-bridged (C2O42-, ox) and mu-chloro-bridged copper(II) network of formula [Cu-2(bpym)(ox)Cl-2](n) is reported. The compound crystallizes in the orthorhombic system, space group Pbca, with a = 9.522(2) Angstrom, b = 10.509(2) Angstrom, c = 13.222(3) Angstrom, Z = 4, and V = 1323.1(5) Angstrom(3). The structure consists of alternatingly mu-bpym- and mu-ox bridged copper(II) chains which again are connected through mono(mu-chloro) ligands, thus forming a corrugated two-dimensional (2D) framework. Polarized optical single crystal absorption spectra, measured at both room and liquid-helium temperatures, are presented and the absorption pattern is discussed using the selection rules derived from an orbital scheme of the Cu(II) chromophore with idealized C-2 upsilon symmetry. A low-lying MLCT state is taken as the origin of the strongly polarized absorption parallel to the b-axis, hence the ox-Cu(II)-bpym direction. The temperature dependence of the magnetic susceptibility is well explained with an alternating chain model, taking into account the strong intramolecular antiferromagnetic interaction through the mu-bpym and mu-ox bridges. The analysis is based on the Hamiltonian, ($) over cap H = -2J Sigma(i=1)(n/2)[($) over cap S-2i.($) over cap S-2i-1 + alpha ($) over cap S-2i.($) over cap S-2i+1], and the resulting exchange parameters are J = -189(1) cm(-1) for the mu-ox link and alpha J = -76(1) cm(-1) for the mu-bpym link, which corresponds to an alternation parameter of alpha = 0.40(2). In addition, a mean- field correction is discussed which considers the possibility of weak "interchain" interactions mediated by the asymmetric mono(mu-chloro) bridges.