The hexagonal close-packed (hcp) Co(0001)/MoS2 and face-centered cubic (fcc) Ni(111)/WSe2 interface atomic, magnetic and electronic structures are investigated using first-principles methods based on the density functional theory. We show that the MoS2 and WSe2 single layers are covalently bond to the Co(0001) and Ni(111) metal surfaces. We describe the consequences of this bonding on the spin magnetic moments and on the electron states at the vicinity of these interfaces, where MoS2 and WSe2 become metallic due to hybridization between Co (or Ni) and S (or Se) atomic orbitals. A finite spin-polarization at the Fermi level is calculated in the MoS2 and WSe2 layers at these two interfaces. We also give and estimation of the Schottky barrier height that may appear at the border between the metallic and semiconducting phases of MoS2 (or WSe2) near the edge of a Co/MoS2 or Ni/WSe2 metallic contact.