As CMOS technologies reach their physical limits, advanced devices and circuit structures are needed to enable compact circuit design. Carbon nanotube field-effect transistors (CNTFETs) are compelling alternatives to MOSFETs, and their ambipolarity provides a route to reduce device count through higher expressive power with dual-gate CNTFETs. However, previous models do not permit switching of the device polarity and the full leveraging of these properties. In this paper, we present the first model that enables the transient simulation of dual-gate ambipolar CNTFET circuits in which the CNTFET polarities can be switched between n- and p-type. This model is based on experimental behavior and is shown to provide an interchangeable source and drain. The utility of the model is then demonstrated through the simulation and analysis of cascaded XOR logic gates and a one-bit full adder that utilize the ability to switch the CNTFET polarity. This model therefore enables the further development of ambipolar CNTFET logic circuits towards their potential replacement of CMOS.