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 mono-atomic halide ligands is novel and results in significantly shorter interlayer distances. Structures were determined by single crystal X-ray diffraction. The isostructural compounds crystallize in the tetragonal space group P4/nbm. [Cu(pyz)2]2+ layers are connected by halide ions along the c-axis and charge is compensated by BF4- ions located in the voids of the 3D coordination network. Temperature dependent X-ray diffraction of 1 revealed the rigidity of the [Cu(pyz)2]2+ layers which 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 around 8 K, indicating quasi 2D antiferromagnetic interactions within the [Cu(pyz)2]2+ layers. 2D Heisenberg model fits result in J|| = 9.4(1) K for 1 and 8.9(1) K for 2. The inter-layer coupling is much weaker with |J| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirm the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through the pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range 3D magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below TN = 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) μB/Cu2+ for 1 and 0.6(1) μB/Cu2+ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the a-b plane and along the c-axis. The anisotropy of the Cu2+ g-tensor was determined from powder and single crystal ESR spectra as gx = 2.060(1), gz = 2.275(1) for 1 and gx = 2.057(1), gz = 2.272(1) for 2 at room temperature.