This paper presents the optimal operation of a building energy management system (BEMS), with combined heat and power (CHP) generation, thermal energy storage (TES), and battery energy storage (BES), subject to load demand uncertainty. The main objective is to reduce the total operating cost (TOC) and total CO2 emission (TCOE). First, we develop two models of load demand forecasting, one for weekday and the other for weekend, using artificial neural networks, long short-term memory, and convolutional neural networks. Then, we incorporate the predicted load demand and load demand uncertainty for planning the energy dispatch of the BEMS. TES aims to store the thermal energy waste from the power generation of CHP and discharge the thermal energy to the absorption chiller to supply the cooling load. BES and spinning reserve (SR) play an important role in handling the uncertainty of the load demand. The operation of BEMS, subject to the load demand uncertainty, is formulated as a linear program. We can efficiently solve the linear program and provide an optimal solution that satisfies the dispatch constraints. Thereafter, we determine the optimal size of BES, based on economics and environmental optimal operation. The proposed BEMS is compared to the previous BEMS, without BES and SR. Furthermore, we propose the multi-objective optimal operation, where the normalization for TOC and TCOE is introduced, and the multi-objective function is defined as a linear combination of normalized TOC and TCOE. The numerical results reveal the trade-off relationship between TOC and TCOE. In particular, when TCOE is minimum, TOC becomes maximum. On the other hand, when TOC is minimum, TCOE becomes maximum. The relationship provides a method to select the operating point, as well as analyze the power flow for the multi-objective optimal operation.