Cooling of commercial buildings contributes significantly to the peak demand placed on an electrical utility grid. Time-of-use electricity rates encourage shifting of electrical loads to off-peak periods at night and weekends. Buildings can respond to these pricing signals by shifting cooling-related thermal loads either by precooling the building's massive structure or by using active thermal energy storage systems such as ice storage. While these two thermal batteries have been engaged separately in the past, this paper investigates the merits of harnessing both storage media concurrently in the context of optimal control. The objective function is the total utility bill including the cost of heating and a time-of-use electricity rate without demand charges. The evaluation of the combined optimal control assumes perfect weather prediction and plant modeling, which justifies the application of a consecutive time block optimization that optimizes 24 hour horizons sequentially. The analysis shows that the combined utilization leads to cost savings that is significantly greater than either storage but less than the sum of the individual savings. The findings reveal that the cooling-related on-peak electrical demand of commercial buildings can be drastically reduced and justify the development of a predictive optimal controller that accounts for uncertainty in predicted variables and modeling mismatch in real time.