A silicon carbide switching device includes a three-terminal interconnected silicon MOSFET and silicon carbide MESFET (or JFET) in a composite substrate of silicon and silicon carbide. For three terminal operation, the gate electrode of the silicon carbide MESFET is electrically shorted to the source region of the silicon MOSFET, and the source region of the silicon carbide MESFET is electrically connected to the drain of the silicon MOSFET in the composite substrate. Accordingly, three-terminal control is provided by the source and gate electrode of the silicon MOSFET and the drain of the silicon carbide MESFET (or JFET). The switching device is designed to be normally-off and therefore blocks positive drain biases when the MOSFET gate electrode is shorted to the source electrode. At low drain biases, blocking is provided by the MOSFET, which has a nonconductive silicon active region. Higher drain biases are supported by the formation of a depletion region in the silicon carbide MESFET (or JFET). To turn-on the device, the gate electrode is biased positive and an inversion layer channel of relatively low resistance is formed in the silicon active region. The channel electrically connects the source of the silicon carbide MESFET (or JFET) with the source of the silicon MOSFET to thereby turn-on the device when a positive drain bias is applied.