Vibrational sum-frequency generation spectroscopy (SFG) is used to characterize the surfaces of beta-HMX single crystals and Estane polymer binder, as well as the HMX-Estane interface. SFG is a nonlinear vibrational spectroscopy that selectively probes vibrational transitions at surfaces and interfaces. On the HMX {011} surface, both CH- and NO2-stretching transitions are observed. Compared to bulk HMX, the surface transitions are blueshifted and the splittings are larger. This effect is explained by surface HMX molecules having partially buried and partially free CH2 and NO2 groups. Estane is a diblock copolymer with both soft and hard segments. Comparison of Estane spectra with polymers having only the soft unit and with polymers having predominantly hard units indicate there is a preference for the hard unit on the surface. SFG spectra of the HMX-Estane interface show smaller splittings of the HMX CH-stretch transitions than at the HMX-air interface, because the partially free surface groups are buried in Estane.