The general features of the neutrino flux from cosmic ray interactions in the Earth's atmosphere are well characterized. However, the absolute precision of calculations is still insufficient and the uncertainty from the modeling of hadronic interactions in the very forward region remains a major limitation. In this work, we benchmark the current generation hadronic models using high-precision atmospheric muon calculations from a few GeV to multiple TeV energies provided by the MCEq code. We derive corrections to hadronic models using publicly available measurements of the flux and charge ratio of atmospheric muons from surface and underground detectors. When combining data, the experimental uncertainties are taken into account. We discuss the calibration method and the strength of the derived constraints.