Public transit ridership has been declining during the past decade in major US cities. Integrating traditional fixed-route transit with more flexible microtransit services has been touted as a means to improve public transit ridership, mobility, accessibility, and sustainable transportation outcomes. However, there are very few successful real-world examples of and guidelines for integrating fixed-route transit and microtransit. To fill this research gap, this thesis proposes an integrated fixed transit and microtransit modeling framework with an agent-based simulation on a multilayer supernetwork to evaluate different network and operation designs. The modeling framework consists of a demand module, which is a binary logit mode choice model for auto and transit modes, where the costs for both modes are calculated by applying a least generalized cost path finding algorithm. The modeling framework also consists of a supply module, which includes an auto network and a transit supernetwork with walking, fixed transit, and microtransit layers. This thesis uses FleetPy, an open-source Mobility-on-Demand (MoD) simulation tool, to model the dynamics of microtransit service and uses the simulation results to update the microtransit layer of the transit supernetwork. This thesis uses the proposed framework to study different design parameters --- fixed-route transit frequencies, microtransit fleet size, virtual stop coverage and operating hours --- as well as their impacts on networks in downtown San Diego and Lemon Grove, a small city in San Diego County. Simulation results show that the proposed framework converges to the mode choice equilibrium and outputs performance metrics of different fixed transit and microtransit designs, including subsidy per transit trip, mode share, jobs accessible within 15 minutes, modal vehicle miles traveled (VMT), individual trip length distribution, and transit line usage. The results imply that introducing new microtransit service decreases fixed-route transit ridership; however, microtransit increases regional accessibility, particularly in areas with limited fixed-route transit coverage, and decreases auto-mode VMT. However, these benefits require significant subsidization.