The interfaces between organic molecules and magnetic metals have gained increasing interest for both fundamental reasons and applications. Among them, the C-60/layered antiferromagnetic (AFM) interfaces have been studied only for C-60 bonded to the outermost ferromagnetic layer [S. L. Kawahara et al., Nano Lett. 12, 4558 (2012) and D. Li et al., Phys. Rev. B 93, 085425 (2016)]. Here, via density functional theory calculations combined with evidence from the literature, we demonstrate that C-60 adsorption can reconstruct the layered-AFM Cr(001) surface at elevated annealing temperatures so that C-60 bonds to both the outermost and the subsurface Cr layers in opposite spin directions. Surface reconstruction drastically changes the adsorbed molecule spintronic properties: (1) the spin-split p-d hybridization involves multi-orbitals of C-60 and top two layers of Cr with opposite spin-polarization, (2) the subsurface Cr atom dominates the C-60 electronic properties, and (3) the reconstruction induces a large magnetic moment of 0.58 mu(B) in C-60 as a synergistic effect of the top two Cr layers. The induced magnetic moment in C-60 can be explained by the magnetic direct-exchange mechanism, which can be generalized to other C-60/magnetic metal systems. Understanding these complex hybridization behaviors is a crucial step for molecular spintronic applications.