We report on a calculation of transport in InAs/GaSb/AlSb‐based interband tunnel structures using a realistic band structure model. The results are compared with calculations using a two‐band model which includes only the lowest conduction band and the light‐hole band. We find that for device structures containing GaSb quantum wells, the inclusion of heavy‐hole states can introduce additional transmission resonances and substantial hole‐mixing effects. These effects are found to have a significant influence on the current–voltage characteristics of interband devices.