We present a high-resolution dissection of the two-dimensional total mass distribution in the core of the Hubble Frontier Fields galaxy cluster MACS J0416.1-2403, at z = 0.396. We exploit HST/WFC3 near-IR (F160W) imaging, VLT/Multi Unit Spectroscopic Explorer spectroscopy, and Chandra data to separate the stellar, hot gas, and dark-matter mass components in the inner 300 kpc of the cluster. We combine the recent results of our refined strong lensing analysis, which includes the contribution of the intracluster gas, with the modeling of the surface brightness and stellar mass distributions of 193 cluster members, of which 144 are spectroscopically confirmed. We find that, moving from 10 to 300 kpc from the cluster center, the stellar to total mass fraction decreases from 12% to 1% and the hot gas to total mass fraction increases from 3% to 9%, resulting in a baryon fraction of approximatively 10% at the outermost radius. We measure that the stellar component represents ∼30%, near the cluster center, and 15%, at larger clustercentric distances, of the total mass in the cluster substructures. We subtract the baryonic mass component from the total mass distribution and conclude that within 30 kpc (∼3 times the effective radius of the brightest cluster galaxy) from the cluster center the surface mass density profile of the total mass and global (cluster plus substructures) dark-matter are steeper and that of the diffuse (cluster) dark-matter is shallower than an NFW profile. Our current analysis does not point to a significant offset between the cluster stellar and dark-matter components. This detailed and robust reconstruction of the inner dark-matter distribution in a larger sample of galaxy clusters will set a new benchmark for different structure formation scenarios.