To investigate the optimal economic dispatch problem with transmission loss for integrated electrical and heating systems, this paper proposes a novel distributed double-consensus based algorithm so as to realize the minimum-cost target by constructing two interactive and paralleled consensus protocols modified with their corresponding time-varying correction terms. Meanwhile, both device models and transmission models are developed together for their practical application significance. Besides, the presented method can not only effectively solve the formulated nonlinear, multi-constrained and coupling optimization problem, but also evenly assign computation and communication burdens to each participant with better robustness and scalability. Finally, simulations performed on six standard case studies are provided to illustrate the effectiveness and satisfying performance of the proposed approach.