•A methodology to analyze the vulnerability of PTSs from the perspective of RC.•The functionality of PTSs is measured by the accessibility of RC.•An algorithm is proposed to calculate the accessibilities of each RC.•The vulnerability of PTSs is analyzed under several daily disruption modes. Public transit systems (PTSs) in a city usually consist of multiple systems with different transit modes, such as bus and subway systems, and the connection relationships among those systems can be described in terms of the geographical proximity of different stations. This paper proposes a methodology to analyze the vulnerability of the PTSs in a city from the perspective of their common functionality of providing residential communities access to critical services, including commuting, medical, commercial and education services. The proposed methodology is built upon a multi-layer network, with each layer describing a particular type of public transit system. This paper applies the proposed methodology to analyze the vulnerability of the bus and subway systems in Wuhan, China, under several types of disruptions, including random vehicle accidents, recurrent traffic jams and a real rainstorm disaster.