Abstract: The transparency of a film/substrate interface for thermal phonons was investigated for YBa2Cu3O7 thin films deposited on MgO, Al2O3, LaAlO3, NdGaO3, and ZrO2 substrates. Both voltage response to pulsed-visible and to continuously modulated far-infrared radiation show two regimes of heat escape from the film to the substrate. That one dominated by the thermal boundary resistance at the film/substrate interface provides an initial exponential decay of the response. The other one prevailing at longer times or smaller modulation frequencies causes much slower decay and is governed by phonon diffusion in the substrate. The transparency of the boundary for phonons incident from the film on the substrate and also from the substrate on the film was determined separately from the characteristic time of the exponential decay and from the time at which one regime was changed to the other. Taking into account the specific heat of optical phonons and the temperature dependence of the group velocity of acoustic phonons, we show that the body of experimental data agrees with acoustic mismatch theory rather than with the model that assumes strong diffusive scattering of phonons at the interface.