In the era of mixed transportation systems, where service-oriented autonomous vehicles (AV) coexist with human-driven regular vehicles (HV), urban transportation network flows will consist of “decentralized” decisions made by commuters who choose the HV mode, and “centralized” decisions made by AV mobility service operators who assign routes to travelers opting for their AV mobility services. This paper presents a hybrid behavior equilibrium model that integrates the combined decision-making processes of elastic demand, traveler service/mode selection, and route allocation/choice, which enriched the theories of mixed networks equilibrium in mixed traffic environment. Two numerical examples are used to verify the effectiveness of the model, revealing that the optimal supply mode for the AV service market is a joint effort between the government and private enterprises. More importantly, this market structure can simultaneously achieve optimal efficiency in the transportation system and minimal perceived unfairness for travelers. This study provides valuable insights into important management questions such as what role the government should play in the AV service market.