The IceCube Neutrino Observatory provides the opportunity to perform unique measurements
of cosmic-ray air showers with its combination of a surface array and a deep detector.
Electromagnetic particles and low-energy muons (∼GeV) are detected by IceTop, while a bundle
of high-energy muons (>~400 GeV) can be measured in coincidence in IceCube. Predictions of
air-shower observables based on simulations show a strong dependence on the choice of the
high-energy hadronic interaction model. By reconstructing different composition-dependent
observables, one can provide strong tests of hadronic interaction models, as these measurements
should be consistent with one another. In this work, we present an analysis of air-shower
data between 2.5 and 80 PeV, comparing the composition interpretation of measurements of
the surface muon density, the slope of the IceTop lateral distribution function, and the energy
loss of the muon bundle, using the models Sibyll 2.1, QGSJet-II.04 and EPOS-LHC. We
observe inconsistencies in all models under consideration, suggesting they do not give an
adequate description of experimental data. The results furthermore imply a significant uncertainty in the determination of the cosmic-ray mass composition through indirect measurements.