Nonequilibrium molecular dynamics (NEMD) simulations have been performed to describe the flow of a fluid nanolayer confined by another fluid. The results show that the behavior of liquids can still be described by the Navier-Stokes equation at the nanoscale, i.e., when only few molecular layers are involved. NEMD furthermore gives additional knowledge on flow. Indeed, while a very small slip is evidenced for a solid-liquid interface as, e.g., in lubrication, the slip lengths are significantly larger at the liquid-liquid interface, as encountered, e.g., in droplet coalescence. The slip lengths of the two fluids are linked. The increase in hydrodynamic slip for liquid-liquid interfaces is attributed to the enhancement of fluid diffusion, which reduces friction.