Shock waves from underwater and air explosions are significant threats to surface and underwater vehicles and structures. Recent studies on the mechanical and thermal properties of various phase-separated elastomers indicate the possibility of applying these materials as a coating to mitigate shock-induced structural failures. To demonstrate this approach and investigate its efficacy, this paper presents a fluid-structure coupled computational model capable of predicting the dynamic response of air-backed bilayer (i.e. elastomer coating – metal substrate) structures submerged in water to hydrostatic and underwater explosion loads. The model couples a three-dimensional multiphase finite volume computational fluid dynamics model with a nonlinear finite element computational solid dynamics model using the FIVER (FInite Volume method with Exact multi-material Riemann solvers) method. The kinematic boundary condition at the fluid-structure interface is enforced using an embedded boundary method that is capable of handling large structural deformation and topological changes. The dynamic interface condition is enforced by formulating and solving local, one-dimensional fluid-solid Riemann problems, which is well-suited for transferring shock and impulsive loads. The capability of this computational model is demonstrated through a numerical investigation of hydrostatic and shock-induced collapse of aluminum tubes with polyurea coating on its inner surface. The thickness of the structure is resolved explicitly by the finite element mesh. The nonlinear material behavior of polyurea is accounted for using a hyper-viscoelastic constitutive model featuring a modified Mooney-Rivlin equation and a stress relaxation function in the form of prony series. Three numerical experiments are conducted to simulate and compare the collapse of the structure in different loading conditions, including a constant pressure, a fluid environment initially in hydrostatic equilibrium, and a two-phase fluid flow created by a near-field underwater explosion.