MBE grown InAs/AlSb heterostructures with AlAs- and InSb-type interfaces were investigated by tunnelling spectroscopy using a scanning tunnelling microscope (STM). STM surface topography revealed a different electronic surface morphology of the thin InAs/AlSb heterostructure in the case of AlAs and InSb interfaces. Scanning tunnelling spectroscopy (STS) gives an understanding of the origin of local morphology fluctuations. STS suggests the occurrence of classical and quantum effects influencing the energy-band-structure formation in the case of these thin heterostructures.