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Shared mobility on demand (MoD) services are receiving increased attention as many high volume ride-hailing companies are offering shared services (e.g. UberPool, LyftLine) at an increasing rate. Also, the advent of autonomous vehicles (AVs) promises further operational opportunities to benefit from these developments as AVs enable a centrally operated and fully connected fleet. There are two fundamental tasks for a shared MoD service: ride-matching and vehicle rebalancing. Traditionally, these two functions are performed sequentially and independently. In this paper, we propose and formulate an integrated ride-matching problem which aims to integrate ride-matching and rebalancing into a single formulation. The integrated problem benefits from interactions between these two tasks. We also propose a methodology to solve the integrated shared ride-matching problem by using supply level information based on a grid representation of the city network. We demonstrate the effectiveness of the proposed methodology through a comparative case study using a benchmark sequential approach and an open source data set. Our results show that the integrated model is able to serve at least the same amount of passengers with significant gains in terms of level of service and sustainability metrics.