This work deals with a coupled acoustic problem involving a compressible fluid and a poroelastic material contained in a cavity whose walls are all rigid except for the top, where a flexible plate is placed. The fluid is described utilizing its acoustic pressure, whereas, for the plate, the Naghdi shell model is used. The mechanical behaviour of the absorbing layer attached to the plate is described by using the Biot-Allard model, where the governing equations are written in the displacement-based formulation. The main novelty of this work lies in addressing the coupling between the plate and the poroelastic medium using the Reissner-Mindlin formulation for the Naghdi’s shell model and the displacement-based formulation for the Biot-Allard model. A comprehensive three-dimensional analysis is performed, comparing numerical and experimental results and showing the advantages of using the Biot-Allard poroelastic model in combination with the Naghdi shell model to predict the in-plane displacements of the plate structure over other fluid-equivalent formulations, such as the Allard-Champoux model.