Langmuir circulation is a convective motion commonly observed in the oceanic mixed layer. Internal waves are a prominent feature of stratified regions, particularly the thermocline bounding the mixed layer. Here, the potential for Langmuir-circulation–internal-wave coupling is investigated using a two-layer ocean model. The density jump across the sharp thermocline confines all rotational motions, including the wind-aligned Langmuir vortices, to the upper (‘mixed’) layer. Linear analysis indicates: (i) that thermocline compliance enhances the onset of Langmuir circulation, and (ii) that the ‘vortex force’ arising from the interaction of surface waves with the wind-driven shear modifies the dynamics of cross-wind propagating internal waves. Weakly nonlinear analysis reveals that resonant cross-wind propagating internal waves can be nonlinearly reflected from stationary Langmuir circulation, a dynamic reminiscent of the ‘Bragg reflection’ of surface waves propagating over sand bars. A key feature of the reflection mechanism is the modification of the linear internal-wave dynamics by the vortex force.