Multiferroic materials with coexisting ferroelectric and ferromagnetic orders have attracted much attention due to the magnetoelectric coupling opening alternative prospects for electronic devices. Composite multiferroics containing separate ferroelectric and ferromagnetic components are a promising alternative to the single-phase counterparts. Composite multiferroic structures comprising HfO2-based ferroelectrics are potentially feasible for technological applications. Here, this study reports on the experiments aiming at the manifestation of magnetoelectric coupling at Fe/Hf0.5Zr0.5O2 (HZO) interface. Using synchrotron based Fe-57 Mossbauer spectroscopy technique in operando, this study probes element-selectively the local magnetic properties of a nanometer-thick enriched Fe-57 marker layer in functional Pt/Fe-57/HZO/TiN capacitors and demonstrates the evidence of the ferroelectric polarization effect on the alpha-Fe magnetic response. Besides alpha-Fe exhibiting a magnetoelectric coupling, both ferromagnetic and superparamagnetic Fe3O4 components are found in the Mossbauer spectra, apparently originating from the oxygen or OH- ions penetrating ultrathin Pt overlayer during crystallization annealing of HZO. The observed effect as well as the electronic band lineup of the Fe/HZO interface elucidated from synchrotron based hard X-ray photoemission spectroscopy measurements are interpreted in terms of charge-mediated magnetoelectric coupling at the Fe/HfO2 interface driven by ferroelectric HZO polarization reversal.