The ice edges of the world ocean are generally the site, at times when winds are blowing off the ice, of regularly spaced surface bands of ice floes. These bands have size scales of the order of 1--10 km, and their long axes are oriented approximately normal to the wind direction. Available oceanic temperature and salinity data from the Bering and Greenland Sea ice edge regions suggest that these ice bands are commonly underlain by a two-layered density structure which is maintained by net melting along the ice edges. Linear internal wave theory is applied to these data to compute first-mode interfacial wave phase speeds. A simple analytical model is developed that demonstrates the feasibility of generation of such interfacial internal waves by the stress discontinuity due to off-ice winds blowing over either a stationary or a moving ice edge. It is qualitatively shown that the computed internal wave phase speeds and wavelengths are, under many conditions, compatible with the speeds and spacings of the surface ice bands. This compatibility suggests, in turn, that coupling between internal waves and ice bands may commonly occur. Some possible implications of the generation and presence of these internal waves upon other ice edge processes, such as air-sea heat and momentum transfer, are qualitatively discussed.