We develop and use a mull-scale averaging technique based on the Lyapunov-Schmidt (L-S) reduction method to obtain reduced order models for monolith reactors with multiple washcoat layers. These models are expressed in terms of phase-averaged concentration modes and inter as well as intra-phase (dispersion) fluxes. The various fluxes are determined by the local equations that are linear in the concentration modes and fluxes. It is shown that the structure of the mull-phase averaged models derived by the L-S method is fundamentally different from the traditional intuitively written models. We provide physical interpretation of the various inter and intra-phase transfer coefficients appearing in the reduced order models and also expressions for them for common geometries. The accuracy of the reduced order models is illustrated by comparing with the exact solutions for selected cases and also with other models in the literature. The usefulness of the reduced order models is illustrated by two examples of dual layered monolith reactors used in diesel oxidation catalysts and hydrocarbon traps.