Ultrasound propagation in porous materials involves some higher order physical parameters whose importance depends on the acoustic characteristics of the materials. This article concerns the study of the influence of two parameters recently introduced, namely, the viscous and thermal surfaces, on the acoustic wave reflected by the first interface of a porous material with a rigid structure. These two parameters describe the fluid/structure interactions in a porous medium during the propagation of the acoustic wave in the high-frequency regime. Both viscous and thermal surfaces are involved in Laurent expansion, which is limited to the dynamic tortuosity and compressibility to a higher order and corrects the visco-thermal losses %Please check intended meaning has been retained. A sensitivity study is performed on the modulus of the reflection coefficient at the first interface as a function of frequency and on the waveforms reflected by the porous material in the time domain. The results of this study show that absorbent porous materials are the most sensitive to viscous and thermal surfaces, which makes the consideration of these two parameters paramount for the characterization of highly absorbent porous materials using the waves reflected from the first interface.