In this work, the temperature-dependent DC performance of InP/GaAsSb double heterojunction bipolar transistors (DHBTs) with an InP/InAlAs composite emitter was characterized. The current transport mechanisms in DHBTs with a type-I InAlAs/GaAsSb emitter-base junction interface and a type-II GaAsSb/InP base-collector were studied. The experimental results reveal that electron injection at emitter-base junction could be affected by conduction barrier limited carrier transport. A conduction band edge discontinuity of 9.5 meV for InAlAs/GaAsSb heterojunction was experimentally estimated.