Ocean surface waves strongly modulate vertical turbulent mixing in the ocean surface boundary layer. When they are aligned with wind-driven shear, Craik-Leibovich instability occurs, generating Langmuir turbulence that strongly enhances vertical mixing. By the same mechanism, they can also stabilize the water column and suppress boundary layer turbulence when they are in opposite direction as the Eulerian current. In this talk, I will demonstrate this stabilizing wave-induced stratification in large eddy simulations under idealized conditions and discuss its effect on vertical mixing. In particular, I will show that a combination of destabilizing surface cooling and stabilizing wave-induced stratification leads to rolls of convective cells aligned perpendicular to Stokes drift. The turbulence intensity in this case is significantly reduced as compared to the case of pure convection. Such stabilizing effect of wave-induced stratification can also be seen under other more realistic conditions, but is missing in existing wave-driven mixing parameterizations. Ideas to incorporate this effect into an ocean vertical mixing parameterization will be discussed.