Integrated energy systems (IES) have emerged as a crucial solution for enhancing energy efficiency and mitigating environmental concerns. However, the impact of inaccuracies in new energy generation and load forecasts on the IES system's dispatch efficiency cannot be ignored. To address this issue, this paper presents a novel multi-timescale scheduling approach for IES, incorporating Power-to-Gas (P2G) devices, and introduces a stepped carbon trading system aimed at curbing carbon emissions. The proposed method takes into account the varying response time scales and prediction errors associated with different energy sources. It establishes distinct dispatch models for day-ahead, intraday, and real-time scheduling. Through comprehensive simulation verification, the study demonstrates that the scheduling model significantly enhances the utilization of new energy resources while concurrently achieving an environmentally friendly and cost-effective system operation. This innovative approach offers an effective means of optimizing IES scheduling, with considerable potential for practical implementation.