The combined cooling, heating and power (CCHP) micro-grids are getting increasing attentions due to the realizations of higher energy efficiency etc. The deepening of electricity market (EM) reforms provides an opportunity for CCHP micro-grid to interact with upstream power grid through participating in EMs while being operated. Hence, the multi-energy operation optimization of CCHP micro-grid should be extended to further involve the strategy of power trading with EMs. This paper proposes a stochastic-robust coordinated optimization model for CCHP micro-grid considering multi-energy operation and power trading with EMs, from the perspective of the day-ahead stage. By depicting the uncertain day-ahead and real-time clearing prices as stochastic scenarios, the objective function is constructed based on stochastic optimization and conditional value-at-risk, which is to minimize both the expected operational cost and potential risk of cost increase related to scenarios. By modeling the uncertain renewable generations as uncertainty set, the operational constraints are established based on robust optimization, which is to guarantee safe and stable operation under the worst-case realizations within uncertainty set. Through the abovementioned combination of multiple methods, the proposed model reasonably keeps both the conservativeness and computational complexity at relatively low levels. Simulations have verified the effectiveness of this model in terms of cost minimization, computational time, renewable power accommodation and risk control compared with existing methods. Furthermore, simulation results also reveal that additional benefits are brought for CCHP micro-grid by EM participations.