This paper studies the tunneling currents in the single-barrier InAs/AlSb/GaSb interband tunneling structures, with an emphasis on correlating with the bandedge alignment. The WKB approximation combined with the k.p two-band model are used to analyze the interband tunneling currents versus the barrier widths to obtained energy level (0.48 +/- 0.1 eV above the valence band maximum of the AlSb) agrees with the valence-band offset between AlSb and GaSb. A good agreement of the peak voltages and the C-V data with the predicted values by the theory using a self-consistent Schrodinger-Poisson solver is obtained, with a value of 0.15-0.2 eV for the InAs/GaSb band overlap.