The recent discovery that specific materials can simultaneously exhibit n-type conduction and p-type conduction along different directions of the single crystal has the potential to impact a broad range of electronic and energy-harvesting technologies. Here, we establish the chemical design principles for creating materials with this behavior. First, we define the single-carrier and multicarrier mechanisms for axis-dependent conduction polarity and their identifying band structure fingerprints. We show using first-principles predictions that the AMX (A = Ca, Sr, Ba; M = Cu, Ag, Au; X = P, As, Sb) compounds consisting of MX honeycomb layers separated by A cations can exhibit p-type conduction in-plane and n-type conduction cross-plane via either mechanism depending on the doping level. We build up the band structure of BaCuAs using a molecular orbital approach to illustrate the structural origins of the two different mechanisms for axis-dependent conduction polarity. In total, this work shows this phenomenon can be quite prevalent in layered materials and reveals how to identify prospective materials.