Measurements of microscale velocity shear in an oceanic, diffusive-convective staircase in an environment with a large applied mean shear are presented. The observed enhancement of shear at high-gradient interfaces separating the homogeneous convecting layers is consistent with stress continuity, where the effective viscosity of the convecting layers is much greater than the viscosity in the interfaces. For the staircase described, the effective mean viscosity is O(10-4) m2 s-1, which is at least an order of magnitude larger than would be expected in the absence of the double-diffusive convection. The dynamic stability of the interfaces, as parameterized by the gradient Richardson number, is reduced significantly by the addition of the enhanced mean shear to the time-dependent interfacial shear that is due to convective eddies in the adjacent layers. Hence, not only the momentum flux but also the scalar (heat and salt) fluxes are increased by the interaction of mean shear with diffusive convection. For the present study, the effective Prandtl number for the staircase is between 1 and 3.