A layered-structure, multifunctional monolith catalyst is provided. The multifunctional monolith catalyst includes a monolithic substrate. A first layer is coated on a surface of the substrate. The first layer includes a first catalyst. A second layer is formed on top of the first layer. The second layer includes a second catalyst, and the second layer is porous. Layering of the first and second catalysts reduces degradation of one or both of the first and second catalysts, and increases a yield of the reaction catalyzed by the second catalyst. A method of converting carbon dioxide to dimethyl ether using the multifunctional monolith catalyst is also provided.