Lunar impact melt deposits have unusual surface properties, unlike any measured terrestrial lava flow. Radar observations suggest that they are incredibly rough at decimeter scales, but they appear smooth in high-resolution, meter-scale optical images. The cause of their unusual surface roughness is unknown. In this work, we investigate the properties of impact melt deposits from seven lunar craters, ranging in size from 7.5 to 96 km in diameter, in an effort to understand the cause of their unique surface texture. We use data from the Lunar Reconnaissance Orbiter's (LRO) Mini-RF instrument to characterize the small-scale roughness of the deposits, data from the LRO Camera (LROC) to characterize their meter-scale morphology, and data from Chandrayaan-1's Moon Mineralogy Mapper (M3) to characterize their composition. This represents the most comprehensive study of the composition of lunar melt deposits completed to date. In particular, we applied a customized spectral unmixing model to the M3 data using laboratory spectra acquired from a range of possible lunar endmembers: pyroxene, olivine, fast-quenched lunar glass simulants, and impact melts and breccias (both synthetic and natural). We found that spectra derived from lunar melt deposits are typically modeled as a mix of the pyroxene and/or impact melts and breccias endmembers. Our modeled results suggest that lunar melt deposits are either crystalline deposits of pyroxene-rich rocks, or a mixture of glassy material and pyroxene minerals. The latter interpretation could explain the roughness observed in the Mini-RF data, if the melt deposits have a glassy surficial layer that shatters during impact gardening to produce decimeter scale blocks.