The design of integrated mobility-on-demand services requires jointly considering the interactions between traveler choice behavior and operators' operation policies to design a financially sustainable pricing scheme. However, most existing studies focus on the supply side perspective, disregarding the impact of customer choice behavior in the presence of co-existing transport networks. We propose a modeling framework for dynamic integrated mobility-on-demand service operation policy evaluation with two service options: door-to-door rideshare and rideshare with transit transfer. A new constrained dynamic pricing model is proposed to maximize operator profit, taking into account the correlated structure of different modes of transport. User willingness to pay is considered as a stochastic constraint, resulting in a more realistic ticket price setting while maximizing operator profit. Unlike most studies, which assume that travel demand is known, we propose a demand learning process to calibrate customer demand over time based on customers' historical purchase data. We evaluate the proposed methodology through simulations under different scenarios on a test network by considering the interactions of supply and demand in a multimodal market. Different scenarios in terms of customer arrival intensity, vehicle capacity, and the variance of user willingness to pay are tested. Results suggest that the proposed chance-constrained assortment price optimization model allows increasing operator profit while keeping the proposed ticket prices acceptable.