This paper presents a new security-constrained multiobjective optimal dispatch (SC-MOOD) framework for an economic and reliable operation of microgrids. The framework is developed based on a computationally effective multiobjective optimization technique, Pareto concavity elimination transformation (PaCcET). The new method considers grid steady-state and dynamic constraints while solving the optimal dispatch in both grid-connected and islanded modes. The constraints consist of power balance, voltage magnitude, line flows, power generation, frequency, and voltage transients. The proposed framework finds the most economic operating solutions to not only minimize the generation cost but also minimize the reliability cost. In this paper, the PaCcET is utilized to solve the SC-MOOD. The PaCcET uses an extraordinary transformation to first transfer all the points from a multiobjective space to a transformed objective space. It then solves a linear combination of transformed objectives using a single-objective optimizer to find all the nondominated points of the original multiobjective space. The performance of the new framework is verified using the simulation results in a microgrid with several distributed energy resources in both grid-connected and islanded modes. The results are then compared with two multiobjective optimization techniques, nondominated sorting genetic algorithm II and multiobjective particle swarm optimization, as two well-known benchmarks.