We study the propagation of combustion waves through porous samples in which two reactions occur. The first is a gasless solid-solid reaction between two solid species in the porous solid matrix to form a solid product, while the second is a solid-gas reaction in which gas delivered to the reaction site through the pores of the sample reacts with one of the solid species to form both solid and gaseous products. We consider the case of coflow filtration, in which the direction of gas flow is the same as the direction of propagation. The gas, consisting of both chemically active and inert components, filters to the reaction zone through the product region thus transferring heat from the high-temperature products to the unburned mixture.