Abstract: The series Sr2MnO2Cu1.5(S1-xSex)(2) (0 <= x <= 1) contains mixed-valent Mn ions (Mn2+/Mn3+) in MnO2 sheets which are separated by copper-deficient antifluorite-type Cu(2-delta)Ch(2) layers with delta similar to 0.5. The compounds crystallize in the structure type first described for Sr2Mn3Sb2O2 and are described in the I4/mmm space group at ambient temperatures. Below about 250 K, ordering between Cu+ ions and tetrahedral vacancies occurs which is long-range and close to complete in the sulfide-containing end member of the series Sr2MnO2Cu1.5S2 but which occurs over shorter length scales as the selenide content increases. The superstructure is an orthorhombic 2 root 2a x root 2a x c expansion in Ibam of the room temperature cell. For x > 0.3 there are no superstructure reflections evident in the X-ray or neutron diffraction patterns, and the I4/mmm description is valid for the average structure at all temperatures. However, in the pure selenide end member, Sr2MnO2Cu1.5Se2, diffuse scattering in electron diffractograms and modulation in high resolution lattice image profiles may arise from short-range Cu/vacancy order. All members of the series exhibit long-range magnetic order. In the sulfide-rich end member and in compounds with x < 0.1 in the formula Sr2MnO2Cu1.5(S1-xSex)(2), which show well developed superstructures due to long-range Cu/vacancy order, the magnetic structure has a (1/4 1/4 0) propagation vector in which ferromagnetic zigzag chains of Mn moments in the MnO2 sheets are coupled antiferromagnetically in an arrangement described as the CE-type magnetic structure and found in many mixed-valent perovskite and Ruddlesden-Popper type oxide manganites. In these cases the magnetic cell is an a x 2b x c expansion of the low temperature Ibam structural cell. For x >= 0.2 in the formula Sr2MnO2Cu1.5(S1-xSex)(2) the magnetic structure has a (0 0 0) propagation vector and is similar to the A-type structure, also commonly adopted by some perovskite-related manganites, in which the Mn moments in the MnO2 sheets are coupled ferromagnetically and long-range antiferromagnetic order results from antiferromagnetic coupling between planes. In the region of the transition between the two different structural and magnetic long-range ordering schemes (0.1 < x < 0.2) the two magnetic structures coexist in the same sample. The evolution of the competition between magnetic ordering schemes and the length scale of the structural order with composition in Sr2MnO2Cu1.5(S1-xSex)(2) suggest that the changes in magnetic and structural order are related consequences of the introduction of chemical disorder.