An integrated energy microgrid (IEM) system consists of power, natural gas, and heat. As the interdependence among different energy utilities grows, there is an urgent need to investigate the combined economic dispatch of the IEM. This paper proposes a convex real-time economic dispatch model for a grid-connected IEM considering ancillary services from diverse resources. The power and gas system models are relaxed by second-order cone programming (SOCP), and the cost function and feasible region of the combined heat and power (CHP) unit are linearly approximated. The effectiveness of the proposed method is verified in the case studies. The cost-effectiveness of enabling energy storage systems (ESSs) to provide ancillary services is demonstrated.