Infrastructure in future smart and connected communities is envisioned as an aggregate of public services, including energy, transportation, and communication systems, all intertwined with each other. The intrinsic interdependency among these systems may exert the underlying influence on both design and operation of the heterogeneous infrastructures. However, few prior studies have tapped into the interdependency among these systems in order to quantify their potential impacts during standard operation. In response to this, this paper proposes an open-source, flexible, integrated modeling framework suitable for designing coupled energy, transportation, and communication systems and for assessing the impact of their interdependencies. First, a novel multi-level, multi-layer, multi-agent approach is proposed to enable flexible modeling of the interconnected systems. Then, for the framework's proof of concept, preliminary component and system-level models for different systems are designed and implemented using Modelica, an equation-based object-oriented modeling language. Finally, three case studies of gradually increasing complexity are presented (energy, energy + transportation, and energy + transportation + communication) to evaluate the interdependencies among the three systems. Quantitative analyses show that the deviation of the average velocity on the road can be 10.5% and the deviation of the power drawn from the grid can be 7% with or without considering the transportation and communication system at the peak commute time, indicating the presence of notable interdependencies. The proposed modeling framework also has the potential to be further extended for various modeling purposes and use cases, such as dynamic modeling and optimization, resilience analysis, and integrated decision making in future connected communities.