This paper proposes a probabilistic model with the aim to reduce the solar energy operation cost and CO2 emissions of a multi-carrier microgrid. The MCMG in this study includes various elements such as combined heat and power (CHP), electrical heat pump (EHP), absorption chiller, solar panels, and thermal and electrical storages. A MILP model is proposed to manage the commitment of energy producers, energy storage equipment, the amount of selling/buying of energy with the upstream network, and the energy consumption of the responsible electrical loads for the day-ahead optimal operation of this microgrid. The proposed operation model is formulated as a multi-objective optimization model based on two environmental and economic objectives, using a weighted sum technique and a fuzzy satisfying approach. In this paper, the 2 m + 1-point estimate strategy has been used to model the uncertainties caused by the output power of solar panels and the upstream power supply price. In order to evaluate the performance of the proposed model, and also for minimizing cost and CO2 emissions, the simulation was conducted on two typical cold and hot days. Numerical results show the proposed model’s performance and the effect of electrifying the heating and cooling of the microgrid through the EHP unit on greenhouse gas emissions in the scenarios considered.