A low-temperature topotactic route is used to assemble metal--anion arrays within a perovskite host. Ion exchange between RbLaNb2O7 and CuX2 (X = Cl, Br) results in a new set of layered copper-oxyhalide perovskites, (CuX)LaNb2O7. Rietveld structural analysis of X-ray powder diffraction data confirms the formation of a two-dimensional copper-halide network in the double-layered perovskite interlayer. This new structure type contains unusual CuO2X4 octahedra that corner-share with NbO6 octahedra from the perovskite slab and edge-share with each other along all four equatorial edges. Magnetic susceptibility measurements show that both products exhibit antiferromagnetic transitions below 40 K. Additionally, these materials are found to be low-temperature phases, decomposing completely by 700 degrees C. The synthetic approach described in this work is significant in that it demonstrates how host structures can be used as templates in the directed low-temperature assembly of extended metal--anion arrays.