The optimal dispatch methods of integrated energy systems (IESs) currently struggle to address the uncertainties resulting from renewable energy generation and energy demand. Moreover, the increasing intensity of the greenhouse effect renders the reduction of IES carbon emissions a priority. To address these issues, a deep reinforcement learning (DRL)-based method is proposed to optimize the low-carbon economic dispatch model of an electricity-heat-gas IES. In the DRL framework, the optimal dispatch model of the IES is formulated as a Markov decision process (MDP). A reward function based on the reward-penalty ladder-type carbon trading mechanism (RPLT-CTM) is introduced to enable the DRL agents to learn more effective dispatch strategies. Moreover, a distributed proximal policy optimization (DPPO) algorithm, which is a novel policy-based DRL algorithm, is employed to train the DRL agents. The multithreaded architecture enhances the exploration ability of the DRL agents in complex environments. Experimental results illustrate that the proposed DPPO-based IES dispatch method can mitigate carbon emissions and reduce the total economic cost. The RPLT-CTM-based reward function outperforms the CTM-based methods, providing a 4.42% and 6.41% decrease in operating cost and carbon emission, respectively. Furthermore, the superiority and computational efficiency of DPPO compared with other DRL-based methods are demonstrated by a decrease of more than 1.53% and 3.23% in the operating cost and carbon emissions of the IES, respectively.