Loads with multi-energy substitution characteristics can improve their own economic benefits and further improve market efficiency due to the ability to participate in the market actively and adjust their own energy purchase plans. However, there is little research on the way of multi-energy load participating in market clearing and the modelling of the relationship between energy purchase plan and energy price at present. Therefore, a complementary elasticity curve that can characterize the correlation between energy price and energy purchase is proposed in this paper to effectively describe the changes in energy purchase demand at different prices based on the modeling of the multi-energy substitution characteristics of the load. The demand side can participate in the market by submitting the volume-price curve directly. On this basis, a clearing model of electricity-gas joint market considering the complementary elasticity of multi-energy loads is proposed, so that the willingness to purchase energy and the characteristics of energy substitution of multi-energy loads are fully considered. Finally, the case study shows that the proposed model can effectively reduce the user's energy purchase price, alleviate the system network congestion and improve the social welfare of the market.