Results of investigations of band structure, Fermi surface and effective masses of charge carriers in the ultrathin (monolayer graphene)/MnO(001) and MnO(001) films are presented using the method of the density functional theory. Features of spin states of valence band and Fermi level as well as an interatomic interaction in these systems are discussed. A magnetic moment at Mn atom is estimated and an effect of spin polarization at atoms of oxygen and carbon has been revealed which natures are discussed. By calculations of structural energies for 2D (monolayer graphene)/MnO(001) and 2D MnO(001) a stability of these systems has been ascertained. In the 2D (monolayer graphene)/MnO(001) and 2D MnO(001) systems the band structure calculations for the 2D systems mentioned above point out that tensor components of effective masses of both electrons and holes are in the ranges of (0.15 - 0.54) <i>m</i>₀ and (0.38 - 1.27) <i>m</i>₀ respectively. Mobility estimations of two-dimensional charge carriers for a 2D (monolayer graphene)/MnO(001)AF2 heterostructure have been performed