Band diagrams and current-voltage and capacitance-voltage characteristics of isotype N+-GaSb/n(0)-GaInAsSb/N+-GaAlAsSb heterostructures have been studied. Dark-current flow mechanisms have been analyzed. It is shown that a staggered type-II heterojunction can behave as a Schottky diode and its current-voltage characteristics exhibit rectifying properties over the entire temperature range 90-300 K. The thermionic-emission current predominates at high temperatures and low voltages. This current is due to thermal excitation of electrons from GaInAsSb to GaSb over the barrier at the heterointerface. A comparison of the relevant theoretical and experimental data confirmed that the tunneling charge transport mechanism plays the key role at low temperatures under both forward and reverse biases.