The forthcoming quantum Internet is poised to allow new applications not possible with the conventional Internet. The ability for both quantum and conventional networking equipment to coexist on the same fiber network would facilitate the deployment and adoption of coming quantum technology. Most quantum networking tasks, like quantum repeaters and the connection of quantum processors, require nodes for multi-qubit quantum measurements (often Bell-State measurements), and their real-world coexistence with the conventional Internet has yet to be shown. Here we field deploy a Measurement-Device Independent Quantum Key Distribution (MDI-QKD) system, containing a Bell-State measurement node, over the same fiber connection as multiple standard Internet Protocol (IP) data networks, between three nearby cities in the Netherlands. We demonstrate over 10 Gb/s classical data communication rates simultaneously with our next-generation QKD system, and estimate 200 GB/s of classical data transmission would be easily achievable without significantly affecting QKD performance. Moreover, as the system ran autonomously for two weeks, this shows an important step towards the coexistence and integration of quantum networking into the existing telecommunication infrastructure.