The possibility for quantum and classical communication to coexist on the same fiber is important for deployment and widespread adoption of quantum key distribution (QKD) and, more generally, a future quantum internet. While coexistence has been demonstrated for different QKD implementations, a comprehensive investigation for measurement-device independent (MDI) QKD - a recently proposed QKD protocol that cannot be broken by quantum hacking that targets vulnerabilities of single-photon detectors - is still missing. Here we experimentally demonstrate that MDI-QKD can operate simultaneously with at least five 10 Gbps bidirectional classical communication channels operating at around 1550 nm wavelength and over 40 km of spooled fiber, and we project communication rates in excess of 10 THz when moving the quantum channel from the third to the second telecommunication window. The similarity of MDI-QKD with quantum repeaters suggests that classical and generalized quantum networks can co-exist on the same fiber infrastructure.