Coupling between electricity systems and heating systems are becoming stronger, leading to more flexible and more complex interactions between these systems. The operation of integrated energy systems is greatly affected, especially when security is concerned. Steady-state analysis methods have been widely studied in recent research, which is far from enough when the slow thermal dynamics of heating networks are introduced. Therefore, an integrated quasi-dynamic model of integrated electricity and heating systems is developed. The model combines a heating network dynamic thermal model and the sequential steady-state models of electricity networks, coupling components, and heating network hydraulics. Based on this model, a simulation method is proposed and quasi-dynamic interactions between electricity systems and heating systems are quantified with the highlights of transport delay. Then the quasi-dynamic interactions were applied using security control to relieve congestion in electricity systems. Results show that both the transport delay and control strategies have significant influences on the quasi-dynamic interactions.