The interactions between transmission and distribution (TD) networks have become extremely important in recent years with the increase of dynamic loads and distributed energy resources (DERs) in the distribution networks that impacts the operation of transmission systems. Since conventional tools can only model and analyze TD networks separately, there is a need for modern modeling tools capable of integrated analysis of these strong TD interactions. To address this need, a TD integration method in ePHASORsim software is presented in this paper utilizing the dynamic Thevenin equivalents. Additionally, ePHASORsim allows users to run these integrated models in real-time, enabling hardware-in-the-loop (HIL) testing of grid optimization and control with real devices. The integrated modeling method was demonstrated using a positive-sequence transmission network modeled in PSS/e with around 7000 buses and an unbalanced three-phase distribution network modeled in CYME with around 3000 nodes. These models were validated individually first and then integrated for dynamic simulation. The integrated model was run in real-time on OPAL-RT's OP5600 simulator with a time step of 10ms and tested successfully for simulation of TD interactions.