A monolithic structure having active material that includes at least inorganic ion exchange material, for purifying a liquid stream of contaminants such as heavy metals, chlorine, volatile organics, pesticides, herbicides, and/or parasites, etc. The structure has an inlet end and an outlet end and a multiplicity of cells extending from inlet to outlet end. The cells are separated from one another by porous walls that are alternatively plugged at each end such that a liquid stream that enters the structure, enters through the unplugged cells at the inlet end and passes through porous walls to be purified by the active material, and thereafter passes out of the structure through unplugged cells at the outlet end. One method of making the structure involves applying active material as a coating on an alternately plugged substrate. The average particle size of the active material after calcination is greater than the average cell wall pore size of the substrate. The coated substrate is dried at no greater than 200° C., and calcined at no greater than 650° C., to bond the active material to the substrate. The structure can be shaped from a forming mixture of the active materials.