In this paper we present an optimized weak coupling of boundary element and finite element methods to solve acoustic scattering problems. This weak coupling is formulated as a non-overlapping Schwarz domain decomposition method, where the transmission conditions are constructed through Padé localized approximations of the Dirichlet-to-Neumann map. The performance of the resulting formulations is analyzed on several three-dimensional examples, with both homogeneous and inhomogeneous scatterers.