We reexamine the problem of inverting C responses, covering periods between 1 month and 1 year collected from 42 European observatories, to constrain the internal structure of the Earth. Earlier studies used the C responses, which connect the magnetic vertical component and the horizontal gradient of the horizontal components of electromagnetic variations, to obtain the conductivity profile of the Earth's mantle. Here, we go beyond this approach by inverting directly for chemical composition and thermal state of the Earth, rather than subsurface electrical conductivity structure. The primary inversion parameters are the composition of the Earth's mantle within the system CaO-FeO-MgO-Al2O3-SiO2 and geotherm. Given these parameters, we calculate mineral modes at the prevailing physical conditions and combine these with laboratory-based models for the conductivity of individual minerals to estimate the bulk Earth electrical conductivity structure from which C responses are calculated. To further constrain the radial density profile, we also invert for mass and moment of inertia. The results agree with earlier geophysically derived conductivity and seismic velocity models and confirm that inversion of geophysical data for compositional parameters, planetary composition, and thermal state is feasible. The inversion indicates most probable lower mantle geothermal gradients of ~0.58 K/km, core mantle boundary temperatures of ~2900¿C, bulk Earth molar Mg/Si ratios of ~1.1, intermediate between the chondrite and pyrolite models, and no significant change in mantle composition across the 670-km seismic discontinuity.