The coupling of acoustics and structural dynamics is of primary importance in the design of MEMS based microphones for use in liquid environments. A three-dimensional finite element study of acoustic-structural coupling is presented here for such a MEMS hydrophone system. The experimental system under consideration, currently under development at Boston University, consists of a horn to amplify incoming sound, a sub-micron thin plate resonator, and a Helmholtz resonator cavity to amplify the measurable response. The finite element results, which consist of steady state pressure fields in the fluid medium and steady state displacements of the resonating plate, compare favorably to experimental results. The effects of acoustic and structural resonances in each of the components of the system are explored, and it is shown that a nonuniform composite plate resonator provides a smoother broadband response in the frequency range of interest than a uniform plate.