Event Relation Extraction (ERE) aims to extract multiple kinds of relations among events in texts. However, existing methods singly categorize event relations as different classes, which are inadequately capturing the intrinsic semantics of these relations. To comprehensively understand their intrinsic semantics, in this paper, we obtain prototype representations for each type of event relation and propose a Prototype-Enhanced Matching (ProtoEM) framework for the joint extraction of multiple kinds of event relations. Specifically, ProtoEM extracts event relations in a two-step manner, i.e., prototype representing and prototype matching. In the first step, to capture the connotations of different event relations, ProtoEM utilizes examples to represent the prototypes corresponding to these relations. Subsequently, to capture the interdependence among event relations, it constructs a dependency graph for the prototypes corresponding to these relations and utilized a Graph Neural Network (GNN)-based module for modeling. In the second step, it obtains the representations of new event pairs and calculates their similarity with those prototypes obtained in the first step to evaluate which types of event relations they belong to. Experimental results on the MAVEN-ERE dataset demonstrate that the proposed ProtoEM framework can effectively represent the prototypes of event relations and further obtain a significant improvement over baseline models.