Integrated electrical, natural gas and district heating (IENGDH) systems considering solar thermal CHP (STCHP) plants and electric boilers, are considered one of the effective way to alleviate the problem of wind and solar curtailments. With the randomness of wind, solar and load taken into account, this paper proposes a risk assessment method for analyzing the IENGDH systems with STCHP plants and electric boilers. In the proposed method, unified steady-state power flow considering the coupling conversion characteristics of STCHP plants and electric boilers is analyzed. Then, an optimization model is achieved to minimize the integrated wind, solar and load curtailments by controlling the characteristics of STCHP plants and electric boilers. The risk levels of wind, solar and load curtailments are effectively assessed and considered in the proposed method. Finally, seven risk indices are proposed to quantify the severity of wind, solar and load curtailments in IENGDH systems. The simulation results of two case studies demonstrate the effectiveness of the proposed method.