This study examines the systemic stability of alternative financial systems alongside traditional ones. Utilizing data from 376 conventional and Islamic financial institutions in South and Southeast Asia, as well as MENA countries, spanning 2000-2019, we analyze systemic risk and potential cross-transmission effects. Initially, we evaluate systemic stability considering both systems as a unified framework, then as separate entities. Subsequently, we investigate distress transmission between them to identify the systemically important financial system in these economies. Our findings suggest that systemic risk in one system may stem from distress in the other, with the conventional system exhibiting greater systemic influence on the Islamic system, while the latter transmits lower systemic shocks to the former. These results remain robust regardless of institution size. Additionally, the Islamic financial system demonstrates greater resilience and lower contagion during the 2008 financial crisis. Ultimately, our findings suggest that Islamic financial institutions complement conventional ones in terms of systemic financial stability in dual-banking systems.