Islamic banking has come to the forefront as being one of the fastest growing branch of the global financial industry in recent years. In this study we evaluate whether coexistence of Islamic and conventional banks promote financial stability. In this respect, we evaluate two types of financial systems: (1) A system solely comprised of conventional banks, (2) a dual system in which conventional and Islamic banks coexist and interact with each other. Accordingly, we design two agent-based models representing aforementioned systems and examine possible contagious effects and causes of bank failures by employing the volatility spillover methodology. We find that Islamic banks greatly promote stability by providing liquidity during financial shocks and create more liquidity per asset compared to conventional banks. We also find that they tend to hold more cash than conventional banks, which cushion the effects of a possible liquidity squeeze. Conventional banks, on the other hand, tend to have reserve deficits, which intensify during shock periods. We conclude that coexistence of both bank types creates a win-win situation and contributes to financial stability.