We propose in the present work an iterative coupling method for a dimensionally heteregeneous problem. We consider the 3D linearized hydrostatic Navier-Stokes equations coupled with corresponding 2D linearized shallow water equations. We first show briefly how to derive the 2D linearized shallow water system from the 3D linearized hydrostatic Navier-Stokes system. Then we propose and study a Schwarz-like algorithm to couple the two systems and we prove under some assumptions that the convergence of this Schwarz algorithm is equivalent to the convergence of the classical domain decomposition algorithm of shallow water equations. Finally, we give some theoretical results related to the control of the difference between a global 3D reference solution and the 3D part of the coupled solution. These results are illustrated numerically.