Superconducting film and substrate interface effects on the response of superconductive edge-transition bolometers are modeled with a one dimensional thermal model in closed form, for samples with large area patterns compared to the substrate thickness. The results from the model agree with experimental results on samples made of meander line patterned granular YBCO films on crystalline substrates, in both the magnitude and phase of the response versus modulation frequency up to about 100 KHz, the limit of the characterization setup. Using the fit of the calculated frequency response curves obtained from the model to the measured ones, values of the film-substrate and substrate-holder thermal boundary resistance, heat capacity of the superconducting film, and the thermal parameters of the substrate materials could be investigated. While the calculated magnitude and phase of the response of the SrTiO3 substrate samples obtained from the model is in a very good agreement with the measured values, the calculated response of the LaAlO3 and MgO substrate samples deviate slightly from the measured values at very low frequencies, increasing with an increase in the thermal conductivity of the substrate material. Using the fit of the calculated response to the measured values, film-substrate thermal boundary resistances in the range of 4.4* 10-3 to 4.4* 10-2 K-cm2-w-1 are obtained for different substrate materials. The effect of substrate optical absorption in the response of the samples is also investigated.