Asymmetric hybrid supercapacitors (AHSCs) combine high specific energy and power by merging two electrodes with capacitive and Faradaic charge storage mechanisms. In this study, we introduce AHSC cells that use lithium titanate and activated carbon electrodes in an alkali-ion containing ionic liquid electrolyte. With this cell concept, it is possible to operate the activated carbon electrode in a higher potential window. Consequently, higher cell voltages and a reduced carbon electrode mass can be used, resulting in significantly increased energy compared to aqueous or organic electrolytes. We demonstrate the feasibility of this cell concept for both lithium- and sodium-ion intercalation, underlining the general validity of our approach. Our prototype cells already reach high specific energies of 100 W h/kg, while maintaining a specific power of up to 2 kW/kg and cycling stability of over 1500 cycles. Owing to the IL electrolyte, stable cycling of an AHSC at 80 °C is demonstrated for the first time.