Results from direct numerical simulations of an unsteady turbulent shear layer with a free surface are presented. The emphasis is on the interaction dynamics of the free surface with the coherent vortices in the underlying turbulent shear flow as well as the resulting free-surface signatures. Instantaneous vortex lines and isosurfaces of enstrophy indicate that coherent horseshoe vortical structures emerge from the random initial vorticity field. These horseshoe vortices impinge, break and reconnect onto the free surface, and then appear as two vortex connections with opposite signs on the surface. The two identified vortical structures correspond to ‘splatting’ and ‘swirling’ events, which have been observed in other experiments and simulations of free-surface/turbulence flows. Though free-surface depressions form near the vertical-vorticity centres in the connection processes, only a low correlation (≈50% to 60%) is found between the free-surface roughness (vertical deformation) and the connected normal vorticity. On the other hand, the free-surface curvatures and the tangential free-surface vorticities are better correlated (≈80% to 90%). The balance of enstrophy and the vorticity transport show that stretching and viscous dissipation along the direction of the vorticity vector dominate the vortex dynamics near the free surface. These two transport mechanisms are found to be responsible for the cancellation of the spanwise vorticity of the horseshoe-vortex heads and the annihilation of the surface-connected normal vorticities.