We have studied the evolution of AlSb-on-InAs(001) surfaces and interfaces grown by molecular-beam epitaxy using in situ scanning tunneling microscopy. We find that forming InSb-like interfacial bonds on an InAs(001)-(2X4) surface creates surface roughness because the surface In coverage inherent to the (2X4) reconstruction is insufficient to form a complete InSb(001)-(1X3)-like surface layer. This morphological roughness can be eliminated by depositing additional In to compensate for the different compositions of the reconstructions. We have also grown three different 5-monolayer-thick films of AlSb on the InSb-like interface to study the effect of growth conditions on the film surface morphology. The AlSb surface can be improved by either raising the growth temperature or by growing the film using migration-enhanced epitaxy. Finally, we present electrical characterization of InAs/AlSb/GaSb resonant interband tunneling devices fabricated with different growth procedures. The possible effects of various growth procedures on interfacial quality and device properties are discussed.