The convergence of various technological and operational advancements has reinstated the interest in On-Demand Air Service (ODAS) as a viable mode of transportation. ODAS enables an end-user to be transported in an aircraft between their desired origin and destination at their preferred time without advance notice. Industry, academia, and the government organizations are collaborating to create technology solutions suited for large-scale implementation of this mode of transportation. Market studies suggest reducing vehicle operating cost per passenger as one of the biggest enablers of this market. To enable ODAS, an ODAS operator controls a fleet of aircraft that are deployed across a set of nodes (e.g., airports, vertiports) to satisfy end-user transportation requests. There is a gap in the literature for a tractable and online methodology that can enable ride-sharing in the on-demand operations while maintaining a publicly acceptable level of service (such as with low waiting time). The need for an approach that not only supports a dynamic-stochastic formulation but can also handle uncertainty with unknowable properties, drives me towards the field of Reinforcement Learning (RL). In this work, a novel two-layer hierarchical RL framework is proposed that can distribute a fleet of aircraft across a nodal network as well as perform real-time scheduling for an ODAS operator. The top layer of the framework - the Fleet Distributor - is modeled as a Partially Observable Markov Decision Process whereas the lower layer - the Trip Request Manager - is modeled as a Semi-Markov Decision Process. This framework is successfully demonstrated and assessed through various studies for a hypothetical ODAS operator in the Chicago region. This approach provides a new way of solving fleet distribution and scheduling problems in aviation. It also bridges the gap between the state-of-the-art RL advancements and node-based transportation network problems. Moreover, this work provides a non-proprietary approach to reasonably model ODAS operations that can be leveraged by researchers and policy makers.