In semiconductor heterostructures with a type II band alignment, such as GaSb-InAs, conduction can be tuned from electron- to hole-dominated using an electrostatic gate. However, traditional conductance measurements give no direct information on the carrier type, and thus limit the ability to distinguish transport effects originating from the two materials. Here, we employ thermovoltage measurements to GaSb/InAs core-shell nanowires, and reliably identify the dominant carrier type at room temperature as well as in the quantum transport regime at 4.2 K, even in cases where the conductance measurement does not allow for such a distinction. In addition, we show that theoretical modeling using the conductance data as input can reproduce the measured thermovoltage under the assumption that electron and hole states shift differently in energy with the applied gate voltage.