This paper focuses on developing an appropriate optimization technique for solving the optimal operation problem of hybrid AC/DC microgrids. A non-linear mathematical formulation is deployed to solve the problem subject to the exhaustive set of constraints and equations pertaining to the operation of AC and DC networks. The proposed approach, being able to capture technical characteristics, such as voltage and frequency, through the detailed power flow algorithm, provides accurate solutions and therefore can address operational challenges of MGs. The approach is applied to a highly-generalizable microgrid comprising of AC and DC generators and loads, as well as storage technologies in order to demonstrate the benefits. The simulation results demonstrate how voltage and frequency are effectively captured across the whole network via the utilised formulation and the power flow through the interlinking converter is associated with frequency (i.e. 49-51 Hz) and voltage variation (i.e. 0.95-1.05 p.u.).