We present a hybrid protocol designed to couple the dynamics of a nanoscopic region of liquid described at atomistic level with a fluctuating hydrodynamics description of the surrounding liquid. The hybrid technique is based on the exchange of fluxes and it is shown to respect the conservation laws of fluid mechanics. This fact allows us to solve unsteady flows involving shear and sound waves crossing the interface of both domains. In equilibrium we find perfect agreement with the grand-canonical ensemble at low and moderate densities, while within the nanoscopic volumes considered, mass fluctuation (both in hybrid and full MD simulations) becomes slightly larger than predicted by the thermodynamic limit. Stress fluctuations across the hybrid interface are shown to have a seamless profile. Nonequilibrium scenarios involving shear (startup of Couette flow) and longitudinal flow (sound waves) are also illustrated.