Maximizing the optimal scheduling capability of a virtual power plant (VPP) over its aggregated resources is crucial for increasing its revenue. However, the limited dispatchable resources in single-energy VPPs hinder maximum economic efficiency. To address this issue, in this paper, a multienergy virtual power plant (MEVPP), which aggregates distributed electrical, thermal, and demand-side flexible resources, is introduced. Furthermore, a low-carbon economic dispatch strategy model is proposed for the coordinated operation of the MEVPP with shared energy storage. First, an MEVPP model incorporating shared energy storage is constructed, with equipment modeling developed from both electrical and thermal dimensions. Second, a low-carbon dispatch strategy that incorporates multiple types of demand responses is formulated, accounting for the effects of electrical and thermal demand responses, as well as carbon emissions, on dispatch. The simulation results demonstrate that, compared with models that do not consider the multienergy demand response, the proposed model reduces system operating costs to 54.2% and system carbon emissions to 42%. Additionally, the MEVPP can leverage energy storage by charging during low-price periods and discharging during high-price periods, thereby enabling low-carbon and economically viable system operation. This study offers valuable insights for the optimized operation of MEVPP systems.