Two Cu2+ coordination polymers [CuCl(pyz)(2)](BF4) 1 and [CuBr(pyz)(2)]-(BF4) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)(2)](2+) magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)(2)](2+) layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at similar to 8 K, indicating antiferromagnetic interactions within the [Cu(pyz)(2)](2+) layers. 2D Heisenberg model fits result in J(parallel to) = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with vertical bar J(perpendicular to)vertical bar = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly sigma-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below T-N = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis (k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) mu(B)/Cu2+ for 1 and 0.6(1) mu(B)/Cu2+ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu2+ g-tensor was determined from electron spin resonance spectra as g(x) = 2.060(1), g(z) = 2.275(1) for 1 and g(x) = 2.057(1), g(z) = 2.272(1) for 2 at room temperature.