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Instantaneous optimization-based energy management systems (EMS) are getting popular since they can yield near-optimal performance in unknown driving situations with minimalistic tuning parameters. However, they often disregard the drivability score of the powertrain as a performance assessment criterion, and this leads to too frequent or even infeasible mode-transitions during the multi-mode operation of a hybrid electric powertrain. Aiming to bring down the mode-transition frequency below a feasible limit, this paper proffers an instantaneous optimization-based EMS, which also accounts for the energy lost during mode-transitions into the cost function along with the electrical and chemical energy losses. The energy lost during a single mode-transition event refers to the summation of change in rotational energy for all the prime-movers, i.e., internal combustion engine and electric machines.