There is an increasing interest in the use of composites for marine/naval structures to reduce weight and maintenance cost, and to improve hydrodynamic and/or structural performance. In particular, recent works suggest that the use of a lightweight, soft core layer can significantly reduce the load transfer to the back layer of a sandwich structure when subjected to shock or impulse loads. The objective of this work is to investigate the role of fluid-structure interaction (FSI) and shock-bubble interaction in the transient response of composite structures during underwater explosions (UNDEX). The spatial distribution of UNDEX loads is different from uniform planar shocks due to the spherically propagating pressure front, and the temporal characteristics are also different due to the importance of shock-bubble interactions. Both effects influence the FSI response of the composite structure. A previously validated 2D Eulerian–Lagrangian numerical method is used to investigate fluid-structure and shock-bubble interaction effects during UNDEX near composite structures. Via a series of numerical experiments, the relative importance of different effects, namely, the Taylor’s FSI effect (1963, “The Pressure and Impulse of Submarine Explosion Waves on Plates” Scientific Papers of G. I. Taylor, 3, pp. 287–303), the bending/stretching effect, the core compression effect, and the boundary effect, are quantitatively and qualitatively evaluated. Insights for practical modeling, analysis, and design of blast-resistant sandwich structures are also drawn from the analysis.