The load profiles of most commercial and industrial consumers are characterized by brief periods of very high power consumption followed by intervals of lower demand. To encourage such consumers to flatten their load profiles, power utilities around the world often levy a monthly demand charge (DC) on the peak demand measured over brief intervals. In this work, we consider the joint optimization of energy costs (EC) and the instantaneous peak power of a multi-unit building which uses a hydronic heating, ventilation and air-conditioning (HVAC) system and responds to a demand response (DR) program. Despite the apparent non-convexity of the control framework, we show how it may be transformed into a convex optimization problem. Next, we study the power demand patterns resulting from our proposed strategy for thermostatically controlled loads (TCLs), and evaluate the strategy’s performance for various climate zones in the US under both typical and atypical weather conditions. The results show that, depending on the ambient conditions and the tariff structure, our strategy can result in utility bill savings of up to nearly 19% compared to the baseline. The results also indicate that our power control strategy can significantly reduce the instantaneous peak power consumption in commercial TCLs.