A fully Lagrangian meshfree computational method is developed for simulation of incompressible fluids interacting with deformable elastic structures. The developed computational method corresponds to a novel SPH (Smoothed Particle Hydrodynamics)-based coupled solver. A projection-based Incompressible SPH (ISPH) fluid model is coupled with a SPH-based structure model in a mathematically-physically consistent manner via a careful attention to the mathematical concept of projection-based particle methods, i.e. Helmholtz-Leray decomposition. The fluid model solves Navier-Stokes and continuity equations, while the structure model is founded on conservation laws for linear and angular momenta corresponding to an elastic solid. A set of previously developed enhanced schemes are incorporated for the ISPH fluid model. Hence, the developed coupled method is referred to as enhanced ISPH-SPH. The performance of structure model is first verified in reproduction of the dynamic response of a cantilever rubber plate and then the enhanced ISPH-SPH is validated through the simulation of two FSI (Fluid-Structure Interaction) problems including a high velocity impact of an elastic aluminum beam, for which semi-analytical solutions exist, and hydroelastic slammings of a marine panel, corresponding to the experiments by Allen (2013).