This work deals with the interaction of waves with a floating structure immersed in a 2D fluid in coastal area. The horizontal plane is decomposed into two regions: the exterior region where the surface of the fluid is in contact with the air, and the interior region where it is in contact with the bottom of the object. In the exterior region, we have the standard equations, where the surface is free but the pressure is constrained (equal to the atmospheric pressure). In the interior region, this is the reverse: the pressure is free but the surface is constrained, which changes the structure of the equations. Finally, coupling conditions between both regions are needed. We show how to implement this program in the case where the waves are described by the nonlinear dispersive Boussinesq equations. We also show a numerical method that exploits the added-mass effect and the dispersive boundary layer.