The influence of the interface roughness in a three-layer metal-adhesive-metal structure on the propagation of shear horizontal waves and more particularly on the transmission coefficient versus the frequency is studied in the particular case of a periodic grating of triangular grooves. For given phonon frequencies, the interaction of an incident shear horizontal mode with the periodical grating gives rise to a retro-converted mode. A numerical finite element simulation permits us to predict the existence of the phonon mode in the three-layer structure and to obtain the evolution of the transmission coefficient around the phonon frequency. An experimental study, based on a generation of waves by a piezocomposite contact transducer and a reception by a laser vibrometer, then confirms these predictions. Finally, a parametric numerical study is performed: the influence of the depth of the roughness and of the number of spatial periods of the grooves on the transmission coefficient is studied.