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. Using kinetics motivated by large activation energy considerations we determine the structure of a uniformly propagating combustion wave and, in particular, such important characteristics as the propagation velocity of the wave, the burning temperature and the composition of the product, which is determined by the proportion of deficient solid reactant converted in each of the two reactions. We observe that the n umber of solutions of the governingequations varies depending on parameters of the system such as gas mass flux, oxidizer concentration in the gas, kinetic characteristics of each reaction, etc.. Finally, we discuss the superadiabatic effect, i.e., how the burning rate is enhanced by coflow filtration, so that e.g., weakly exothermic gasless systems which would not burn, now do so due to filtration.