By applying van de Walle and Martin's model solid theory (MST), we have investigated the compositional dependence of the band-edge alignment at the AlxGal-xSbAs/InGaAs and AlxGal-xSbAs/InAlAs hoterointerfaces lattice-matched to InP. A comparison between theoretical calculations and previously published experimental values on tertiary extremes of AlxGal xSbAs yields a discrepancy of 0.1-0.2 eV for GaSbAs/InAlAs and GaSbAs/InGaAs, and 0.3 eV for AlSbAs/InAlAs and AlSbAs/InGaAs. For all four heterostructures, it has been found that the MST results shift the valence band edge of the (Sb, As) alloy downward relative to that of InAlAs and [nGaAs as compared to experimental data. and possible causes of the disagreement are analyzed. Furthermore, the band offset values have been obtained from a current-voltage measurement on [nGaAs/AlxGal-xSbAs/InGaAs seiniconductor-insulator-semiconductor diodes. The carrier transport mechanism in these diodes is discussed and the measured offset values are shown to be in qualitative agreement with the MST predictions.