Existing activity-based and agent-based simulations alone often failed to capture the interaction between individual activity scheduling and detailed urban traffic dynamics. ActivitySim provides a representation of individual activity schedulings but often lacks detailed traffic dynamics, whereas MATSim can capture detailed interactions between travellers and mobility systems but often overlooks several decision-making factors, such as activity scheduling shift, household interactions and land-use influences. To address these limitations, this paper presents an Activity- and Agent-based Co-simulation framework that integrates ActivitySim and MATSim, both of which are open-source software popularly adopted in each research community. ActivitySim generates individual activity schedules and location choices, which serve as synthetic travel demand input for MATSim. MATSim then simulates detailed mobility interactions, with its outputs aggregated into zonal level-of-service matrices and fed back to ActivitySim for iterative scheduling adjustments. The feedback loop bridges the strengths of both models and is applied to the MRDH (Rotterdam-The Hague Metropolitan) region in the Netherlands. The initial MRDH model for the base-year reference scenario demonstrates that the proposed co-simulation framework effectively replicates existing mobility patterns, paving the way for fine-grained intervention evaluations like ride-hailing services in the future.