This research effort formulates and solves a biobjective dynamic combined heat and power economic-emission dispatch (DCHPED) of generation in a microgrid (MG). The MG encompasses fossil-fuel power and heat units, renewable resources, price-operated electrical and thermal energy storage elements, bidirectional-exchange of electrical power with the external grid, and fixed nondefferrable and deferrable loads. The two objective functions involve the total operation cost and the total gas emission produced by the fossil fuel units participating in the MG dynamic dispatch. Costs of emission tax and price-based energy storage and exchanges with the external grid are ingredients of the total operating costs. The Bernstein-search differential evolution (BSDE) algorithm is utilized to deal with the problem to obtain the day-ahead optimal schedules of available resources. The nonlinear nonconvex MG DCHPED optimization problem that has a large number of decision variables involves equality and inequality constraints, production costs, emission levels, taxes of released gases, ramp-rate limits of power-producing units, effects of valve-points in generating units, active power transmission losses, and feasible operation regions of cogenerating (CHP) units. The paper investigates the positive impacts of utilizing price-based electrical and thermal storage elements, deferrability of loads, and price-based power exchanges on the day-ahead MG operation cost. The paper also describes an approach to achieve the best compromise solution (BCS) of the MG DCHPED employing the fuzzy satisfying method (FSM). In addition, it shows that gas emissions and emission taxes in the MG can be both controlled by exchanging power with the external grid.