The characteristics of GaSb/AlSb/InAs/GaSb/AlSb/InAs broken-gap interband tunneling structures are investigated. In addition to the main negative differential resistance peaks, kinks or small peaks can be clearly seen, especially at low temperature. The effects of the heavy-hole states are expected to play an important role. Here, a k·p model incorporating the coupling effects of the heavy-hole states is used. It is found that the kinks and small peaks are the results of heavy-hole coupling. Furthermore, the electron distribution in the InAs emitter also contributes to the phenomena observed in the low-temperature characteristics.