A natural medium for  wave propagation comprises a  coupled bounded heterogeneous region  and an  unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation,  include a faraway decay  radiation condition (RC).   It is desirable to develop algorithms that  incorporate  the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of  the  RC. In this talk we first discuss  a new overlapping decomposition framework  that is equivalent to the full-space  heterogeneous-homogenous  continuous  model,  governed by the Helmholtz equation with a spatially dependent refractive index  and the RC. Subsequently, we describe an efficient  FEM-BEM algorithm for  the equivalent wave propagation model in heterogenous and unbounded media.