Machine learning techniques have been extensively developed in the field of electricity theft detection. However, almost all typical models primarily rely on electricity consumption data to identify fraudulent users, often neglecting other pertinent household information such as gas consumption data. This article aims to explore the untapped potential of gas consumption data, a critical yet overlooked factor in electricity theft detection. In particular, we perform theoretical, qualitative, and quantitative correlation analyses between gas and electricity consumption data. Then, we propose two model-agnostic frameworks (i.e., multichannel network and twin network frameworks) to seamlessly integrate gas consumption data into machine learning models. Simulation results show a significant improvement in model performance when gas consumption data are incorporated using our proposed frameworks. Also, our proposed gas and electricity convolutional neural network, based on the proposed framework, demonstrates superior performance compared to classical and recent machine learning models on datasets with varying fraudulent ratios.