Double-diffusive convection may occur if both temperature and salinity increase with depth, as in the Arctic Ocean. The process is identifiable by a staircase structure, with mixed layers separated by high-gradient interfaces in temperature and salinity. These staircases, which persist if turbulence levels are weak, are widely present in the Arctic Ocean and responsible for transporting heat toward the overlying sea ice. Acoustic observations (reflection coefficients) from a broadband echo sounder are analyzed here to track the detailed evolution of interfaces in the Arctic's double-diffusive staircase. We infer interface thicknesses from reflection coefficient profiles and find that thicknesses appear to be related to water column displacements. Further, we relate reflection coefficients to interface stratification and interpret stratification changes in the context of turbulence acting to thicken interfaces. The high-resolution capabilities of the echo sounder allow for insights into how double-diffusive heat fluxes and inferred mixing levels may vary in space/time.