We have used in situ plan-view scanning tunneling microscopy to study the surfaces and interfaces within an InAs/AlSb/InAs resonant tunneling diodelike structure grown by molecular beam epitaxy. The nanometer and atomic-scale morphologies of the surfaces have been characterized following a number of different growth procedures. When InAs(001)-(2 x 4) is exposed to Sb-2 a bilayer surface is produced, with 1 monolayer (ML) deep (3 Angstrom) vacancy islands covering approximately 25% of the surface. Both layers exhibit a (1 x 3)-like reconstruction characteristic of an InSb-like surface terminated with >1 ML Sb, indicating that there is a significant amount of Sb on the surface. When 5 ML of AlSb is deposited on an Sb-terminated InAs surface, the number of layers observed on each terrace increases to three. Growth of an additional 22 ML of InAs onto the AlSb layer, followed by a 30 s interrupt under Sb-2, further increases the number of surface layers observed. The root-mean-square roughness is found to increase at each subsequent interface; however, on all the surfaces the roughness is less than or equal to 2 Angstrom. The surface roughness is attributed to a combination of factors, including reconstruction-related stoichiometry differences, kinetically limited diffusion during growth, and lattice-mismatch strain. Possible methods to reduce the roughness are discussed.