Abstract: Sr2CrO2Cr2As2 and Ba2CrO2Cr2As2 with Cr2+ ions in CrO2 sheets and in CrAs layers crystallize with the Sr2Mn3Sb2O2 structure (space group I4/mmm, Z = 2) and lattice parameters a = 4.00800(2) Å, c = 18.8214(1) Å (Sr2CrO2Cr2As2) and a = 4.05506(2) Å, c = 20.5637(1) Å (Ba2CrO2Cr2As2) at room temperature. Powder neutron diffraction reveals checkerboard-type antiferromagnetic ordering of the Cr2+ ions in the arsenide layers below TN1Sr, of 600(10) K (Sr2CrO2Cr2As2) and TN1Ba 465(5) K (Ba2CrO2Cr2As2) with the moments initially directed perpendicular to the layers in both compounds. Checkerboard-type antiferromagnetic ordering of the Cr2+ ions in the oxide layer below 230(5) K for Ba2CrO2Cr2As2 occurs with these moments also perpendicular to the layers, consistent with the orientation preferences of d4 moments in the two layers. In contrast, below 330(5) K in Sr2CrO2Cr2As2, the oxide layer Cr2+ moments are initially oriented in the CrO2 plane; but on further cooling, these moments rotate to become perpendicular to the CrO2 planes, while the moments in the arsenide layers rotate by 90° with the moments on the two sublattices remaining orthogonal throughout [behavior recently reported independently by Liu et al. [Liu et al. Phys. Rev. B 2018, 98, 134416]]. In Sr2CrO2Cr2As2, electron diffraction and high resolution powder X-ray diffraction data show no evidence for a structural distortion that would allow the two Cr2+ sublattices to couple, but high resolution neutron powder diffraction data suggest a small incommensurability between the magnetic structure and the crystal structure, which may account for the coupling of the two sublattices and the observed spin reorientation. The saturation values of the Cr2+ moments in the CrO2 layers (3.34(1) μB (for Sr2CrO2Cr2As2) and 3.30(1) μB (for Ba2CrO2Cr2As2)) are larger than those in the CrAs layers (2.68(1) μB for Sr2CrO2Cr2As2 and 2.298(8) μB for Ba2CrO2Cr2As2) reflecting greater covalency in the arsenide layers.