  We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method
for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise
mass-conserving discretization resulting in a divergence-conforming velocity
field on the whole domain. In the proposed scheme, coupling between the Stokes
and Darcy domains is achieved naturally through the EDG-HDG facet variables.
\emph{A priori} error analysis shows optimal convergence rates, and that the
velocity error does not depend on the pressure. The error analysis is verified
through numerical examples on unstructured grids for different orders of
polynomial approximation.
