Optimal scheduling of a redundant residential microgrid (RR-microgrid) could yield economical savings and reduce the emission of pollutants while ensuring the comfort level of users. This paper proposes a novel multi-objective optimal scheduling method for a grid-connected RR-microgrid in which the heating/cooling system of the RR-microgrid is treated as a virtual energy storage system (VESS). An optimization model for grid-connected RR-microgrid scheduling is established based on mixed-integer nonlinear programming (MINLP), which takes the operating cost (OC), thermal comfort level (TCL), and pollution emission (PE) as the optimization objectives. The non-dominate sorting genetic algorithm II (NSGA-II) is employed to search the Pareto front and the best scheduling scheme is determined by the analytic hierarchy process (AHP) method. In a case study, two kinds of heating/cooling systems, the radiant floor heating/cooling system (RFHCS) and the convection heating/cooling system (CHCS) are investigated for the RR-microgrid. respectively, and the feasibility and validity of the scheduling method are ascertained.