A novel method for studying the quantitative characteristics of combustion wave microstructure has been developed. Using the combustion of titanium and silicon powders as an example, the propagation of the combustion wave at the scale of microscopic heterogeneity is examined quantitatively for the first time. The variations in time and space of the combustion wave shape and propagation are studied experimentally. The sample porosity and the refractory reactant particle size are found to affect the heterogeneity of the combustion wave. For low porosities and small particle sizes, the shape and propagation of the combustion wave at the microscopic level approach that observed at the macroscopic level. However, for high porosities and large particle sizes, significant dispersion of the combustion front and local instantaneous velocities is observed at the microscopic level. A new relay-race mechanism of combustion wave propagation, that accounts for the heterogeneity of the reactant medium, is suggested.