To address the issues of high current stress and poor dynamic response in hybrid three-level dual active bridge (DAB) converters, this study proposes an improved extended phase-shift (EPS) modulation scheme and a minimum current stress control strategy based on a super-twisting sliding mode active disturbance rejection controller (STSMC-ADRC). First, the EPS modulation is enhanced by redefining the internal and external phase-shift ratios, ensuring a positive correlation between the phase-shift ratios and transmitted power while reducing coupling between the ratios. Second, mathematical models of transmitted power and current stress under different operating modes are analyzed for the improved EPS modulation. The karush-kuhn-tucker (KKT) conditions are applied to solve for the optimal phase-shift ratio combination that minimizes current stress while satisfying soft-switching constraints. Third, to simplify calculations, a reduced-order model of the converter is established, and the super-twisting sliding mode control algorithm is integrated with active disturbance rejection technology to enhance dynamic performance. Finally, experimental validation is conducted using a prototype. Results demonstrate that compared to traditional ADRC, the proposed STSMC-ADRC reduces the regulation time by 72.4% and voltage fluctuation by 51.7% during sudden load resistance reduction. For input voltage step changes, the regulation time is shortened by 73.7% and voltage fluctuation decreased by 60%. Additionally, the strategy effectively reduces current stress and achieves soft switching. Compared to single phase-shift modulation, efficiency improves by 15% at low power and 9% at high power.