This paper deals with the multi-objective economic-emission dispatch problem of combined heat and power (CHP) generation in a large microgrid (MG). The MG comprises many types of fossil fuel generating units, wind power units, and solar power units. The objective functions involve unit operating costs, emission level, emission tax, and cost of power purchase from the main external grid. Interdependencies of heat and power outputs of CHP units and valve-point effects of thermal units impose non-convexities, nonlinearities and complications in the dispatch modeling and optimization. The intermittent stochastic nature of wind and solar power and considering transmission losses increase the complexity of the problem. In addition to compromise programming, this paper uses some recent metaheuristic methods to solve the MG combined heat-power economic-emission dispatch (MG CHPED) problem. The results will show that cost and emissions in MG are totally conflicting functions, and different global optimization solvers may result in different near-global solutions. Single and multi-objective solutions obtained for the MG CHPED require the MG operator to use a decision-making tool, which is the fuzzy satisfying method in this paper, to select the best compromise solution among the achieved sets of solutions.