The possibility for quantum and classical communication to coexist on the\nsame fibre is important for deployment and widespread adoption of quantum key\ndistribution (QKD) and, more generally, a future quantum internet. While\ncoexistence has been demonstrated for different QKD implementations, a\ncomprehensive investigation for measurement-device independent (MDI) QKD -- a\nrecently proposed QKD protocol that cannot be broken by quantum hacking that\ntargets vulnerabilities of single-photon detectors -- is still missing. Here we\nexperimentally demonstrate that MDI-QKD can operate simultaneously with at\nleast five 10 Gbps bidirectional classical communication channels operating at\naround 1550 nm wavelength and over 40 km of spooled fibre, and we project\ncommunication rates in excess of 10 THz when moving the quantum channel from\nthe third to the second telecommunication window. The similarity of MDI-QKD\nwith quantum repeaters suggests that classical and generalised quantum networks\ncan co-exist on the same fibre infrastructure.\n