Multi-energy virtual power plant (MEVPP) with diversified flexible resources can participate in energy market (EM), frequency regulation market (FRM) and carbon trading market (CM) to obtain extra benefits. However, the complicated market environment provokes grant challenges in the bidding strategy of MEVPP that coordinates heterogenous supply-side devices and demand-side users. To the end, this study proposes a multi-objective bidding strategy for MEVPP comprising various energy flows and multi-energy demand response (MDR) in EM, FRM and CM. Results are delivered that: 1) Compared to the only profit-oriented optimization, the profit of comprise solution under the multi-objective declines by 46% but the satisfaction level improves 8%. Relative to the single satisfaction-oriented optimization, a 5.2% satisfaction loss allows for an approximately 103% growth in profit, realizing a win-win result for MEVPP and users. 2) There were negative profits in the pure EM (Case 1) as well as EM and CM (Case3). Compared with positive profit in EM and FRM (Case 2), the profit in coupled EM, FRM and CM (Case 4) increases by 48.9%. Relative to the CO2 emission in EM and CM, the emission under the proposed strategy mitigates by 9.36%. 3) A carbon base price at 200 CNY/t CO2 and an emission interval length of 5-10 t are recommended to maintain the low-carbon economic operation for MEVPP.