With the penetration of distributed energy resources, peer-to-peer (P2P) energy trading is becoming a promising way to harmonize the decarbonization and decentralization transformations in the energy sector. P2P markets give peers the autonomy to make individual decisions and cooperative behaviors between the peers may emerge. However, existing studies on cooperative behaviors in P2P markets focus mostly on the electricity sector, P2P multi-energy markets are rarely studied. In fact, other energy carriers not only constitute a large part of the total energy demand, but their coupling can potentially benefit the system as well as the end-users. In this paper, we propose a P2P multi-energy market mechanism that allows peers to trade both electricity and heat, where the peers can join two predefined trading coalitions. The proposed system model thus explores the integrated effects of the multi-energy coupling and the cooperative behaviors in the P2P market. In order to maximize the net benefits of the peers, price conditions are derived, based on which the peers will join either of the coalitions and determine their trading volumes. Then, the electricity and the heat markets are cleared separately by a market operator. Lastly, the market mechanism is illustrated by a case study on a neighborhood in the Netherlands using realistic data.