The study of wave propagation in fluid-solid media is vital for various disciplines ranging from geophysics and ocean acoustics to biomedical applications. A great number of studies have focused on this topic, yet the computationally efficient and accurate solution of 3-D wavefields with broadband spectrum in complex stratified fluid-solid media remains extremely challenging. A discrete version of the normal modes approach is introduced in this work for the dynamic analysis of arbitrarily layered acousto-elastic domains, namely the Thin-Layer Method (TLM) (Kausel, 1999). The TLM has been successfully implemented in various engineering problems, with main focus on the fields of seismology, earthquake engineering and soil-structure interaction. The main advantages of the method lie in the seamless treatment of arbitrarily layered domains, its reliance on standard and widely accessible numerical algorithms (i.e. linear eigenvalue solver) and the derivation of explicit expressions with integral transforms that are analytically tractable. In this paper, the Green's functions are presented for a variety of axisymmetric and non-axisymmetric sources acting within the fluid or the solid layers of horizontally stratified acousto-elastic media. Furthermore, the applicability of the method is further extended by incorporating Perfectly Matched Layers (PMLs), to approximate fluid and/or solid half-spaces (de Oliveira Barbosa et al., 2012). The numerical results obtained via the TLM are validated against Finite Element (FE) simulations performed in COMSOL Multiphysics (COMSOL AB, 2022). Conclusively, the TLM is demonstrated as a superbly efficient method for the analysis of wave motion in acousto-elastic media, showcasing its vast potential for application in the field of underwater acoustics.