We present a detailed theoretical study on the features of band hybridization and zero-field spin-splitting in InAs/AlSb/GaSb quantum wells (QWs). An eight-band k⋅p approach is developed to calculate the electronic subband structure in such structures. In the absence of the AlSb layer, the hybridized energy gaps can be observed at the anticrossing points between the lowest electron subband and the highest heavy-hole subband in the InAs and GaSb layers respectively. In such a case, the position and magnitude of the gaps are spin-dependent. When a thin AlSb layer is inserted between the InAs and GaSb layers, we find that the lowest electron subband in the InAs layer is only hybridized with the highest light-hole subband which is also hybridized with the highest heavy-hole subband in the GaSb layer. The hybridized energy gaps and spin-splitting in the InAs/AlSb/GaSb QWs are reduced significantly. These results can be used to understand why electrons and holes can be well separated and why relatively high mobilities for electrons and holes can be achieved in InAs/AlSb/GaSb type II and broken-gap QWs. The present study is relevant to the applications of InAs/GaSb based QW structures as new generation of high-density and high-mobility electronic devices.