Porous media combustion is a promising combustion technology that enables operation over an extended range of conditions, with a variety of fuels and low pollutant emissions. However, the lack of understanding of the interstitial combustion processes remains a major obstacle towards the application of this technology and the development of predictive models. To understand these processes, this study presents an integrated experimental and computational effort to examine porous media combustion. Specifically, a new experimental diagnostic method is employed that simultaneously combines synchrotron X-ray micro-computed tomography (μCT) and short-wavelength infrared thermometry. With this approach, the surface temperature and the 3D gas-phase temperature field are simultaneously measured inside a porous burner with micrometer spatial resolution. These measurements are then integrated into 3D pore-resolved simulations. This integrated approach enables a direct evaluation of current modeling capabilities, and a unique analysis of interstitial combustion in porous foams under realistic heating conditions. In light of these results, we discover that about 80% of the fuel consumption inside the matrix pores occurs far enough from the porous surface to be characteristic of a decoupled regime of preheated, but adiabatic flamelets. The remaining fuel consumption near the pore surface occurs in a non-adiabatic combustion mode. This insight and the proposed approach contribute to our fundamental understanding of porous media combustion, and suggest that multi-regime models could more accurately describe porous burners.