The three-dimensional hybrid organic-inorganic perovskites have shown huge potential for use in solar cells and other optoelectronic devices. Although these materials are under intense investigation, derivative materials with lower dimensionality are emerging, offering higher tunability of physical properties and new capabilities. Here, we present two new series of hybrid two-dimensional (2D) perovskites that adopt the Dion-Jacobson (DJ) structure type, which are the first complete homologous series reported in halide perovskite chemistry. Lead iodide DJ perovskites adopt a general formula A'A Pb I (A' = 3-(aminomethyl)piperidinium (3AMP) or 4-(aminomethyl)piperidinium (4AMP), A = methylammonium (MA)). These materials have layered structures where the stacking of inorganic layers is unique as they lay exactly on top of another. With a slightly different position of the functional group in the templating cation 3AMP and 4AMP, the as-formed DJ perovskites show different optical properties, with the 3AMP series having smaller band gaps than the 4AMP series. Analysis on the crystal structures and density functional theory (DFT) calculations suggest that the origin of the systematic band gap shift is the strong but indirect influence of the organic cation on the inorganic framework. Fabrication of photovoltaic devices utilizing these materials as light absorbers reveals that (3AMP)(MA)PbI has the best power conversion efficiency (PCE) of 7.32%, which is much higher than that of the corresponding (4AMP)(MA)PbI.