The aim of this paper is to provide an analytical contribution which presents the application of shear-horizontal (SH)-guided waves for the characterisation of a bi-layered structure which consists of two isotropic plates adhesively bonded using a non-dissipative thin layer of glue. The thickness of the layer of glue is assumed to be non-negligible, and the interfaces between this layer of glue and the plates are both assumed to be roughened (parallel ridges with complex shape and depth profiles). The basis of the theoretical approach is an extension of the integral formulation, in the frame of SH modal couplings due to the roughness, which has been developed previously for SH-wave propagation over a single plate with a rough surface. This approach assumes that the average roughness height is a small fraction of the thicknesses of the waveguides (the plates) everywhere. The changes, due to the roughness, in the characteristics of the fields created by a harmonic source set at the entrance edge of the structure are expressed through the mapping of the displacement and stress perturbations. Preliminary tests of the effectiveness of the model are given; they rely on the phase-matching effects of periodic profiles and pseudo-random experimental profile.Read less <