Video conferencing applications pose fundamentally different service requirements than traditional data traffic on the Internet. Strong real-time interactivity is very important among participants unlike video streaming in VoD applications. Requirements are even more stringent in multi-stream and multi-site teleimmersive applications due to strong dependencies across geographically distributed streams. In this paper, we propose OpenSession, a cross-layer session-network control protocol for multi-stream multi-site 3D teleimmersion (3DTI) that improves interactivity, resource utilization and scalability. OpenSession decouples application layer data and control plane functionalities, and partially offloads the data plane functionalities to network layer switches. To control network layer switches during the session run-time, OpenSession leverages support from Software Defined Networking (e.g., OpenFlow). Through extensive evaluation with multi-stream 3D teleimmersion among four distributed sites and PlanetLab-based larger 3DTI setup, we show that OpenSession improves 3DTI interactivity and resource usage at the data plane. Furthermore, OpenSession keeps data plane robust against host failures and frequent route updates.