Scanning tunneling microscopy and spectroscopy is used to characterize InAs/GaSb superlattices, grown by molecular-beam epitaxy. Roughness at the interfaces between InAs and GaSb layers is directly observed in the images, and a quantitative spectrum of this roughness is obtained. Electron subbands in the InAs layers are resolved in spectroscopy. Asymmetry between the interfaces of InAs grown on GaSb compared with GaSb grown on InAs is seen in voltage-dependent imaging. Detailed spectroscopic study of the interfaces reveals some subtle differences between the two in terms of their valence-band onsets and conduction-band state density. These differences are interpreted in a model in which the GaSb on InAs interface has an abrupt InSb-like structure, but at the InAs on GaSb interface some Sb grading occurs into the InAs overlayer.