In this paper we construct an accurate linear model describing the propagation of both acoustic and gravity waves in water. This original model is obtained by the linearization of the compressible Navier-Stokes equations with free surface written in Lagrangian coordinates accounting for vertical variations of the background temperature and density. The models from the literature can be obtained from our model through two asymptotic analysis, one for the incompressible regime and one for the acoustic regime. We also propose a method to write the model in Eulerian coordinates. Our model includes many physical properties, such as the existence of internal gravity waves or the variation of the sound speed with depth.