Thermal transport in polymer nanocomposites becomes dependent on the interfacial thermal conductance due to the ultra-high density of the internal interfaces when the polymer and filler domains are intimately mixed at the nanoscale. However, there is a lack of experimental measurements that can link the thermal conductance across the interfaces to the chemistry and bonding between the polymer molecules and the glass surface. Characterizing the thermal properties of amorphous composites are a particular challenge as their low intrinsic thermal conductivity leads to poor measurement sensitivity of the interfacial thermal conductance. To address this issue here, polymers are confined in porous organosilicates with high interfacial densities, stable composite structure, and varying surface chemistries. The thermal conductivities and fracture energies of the composites are measured with frequency dependent time-domain thermoreflectance (TDTR) and thin-film fracture testing, respectively. Effective medium theory (EMT) along with finite element analysis (FEA) is then used to uniquely extract the thermal boundary conductance (TBC) from the measured thermal conductivity of the composites. Changes in TBC are then linked to the hydrogen bonding between the polymer and organosilicate as quantified by Fourier-transform infrared (FTIR) and X-ray photoelectron (XPS) spectroscopy. This platform for analysis is a new paradigm in the experimental investigation of heat flow across constituent domains.