In the analysis of the operational reliability of integrated electrical energy systems, traditional numerical algorithms for solving natural gas dynamics require a substantial amount of computation, making it challenging to complete the analysis within operational time scales. This paper proposes a novel method: replacing traditional numerical methods with a CNN-LSTM neural network algorithm. The algorithm first utilizes a Convolutional Neural Network (CNN) for feature extraction, followed by a Long Short-Term Memory network (LSTM) for feature sequence prediction. Through a sequence-to-sequence learning process, the model learns the mapping relationships between adjacent time steps from the data, constructing a dynamic surrogate model for the gas network. This dynamic surrogate model is further integrated with the power system load flow model, combined with Monte Carlo simulation and multi-state models, to comprehensively analyze the operational reliability of integrated electrical energy systems. In the validation phase, the proposed model was applied to a distribution network-level electric-gas integrated energy system. The validation results demonstrate that the model not only accurately simulates the complex characteristics of gas network dynamics but also significantly reduces the computation time for operational reliability.