The discovery of superconductivity at 80 K under high pressure in La3Ni2O7 3 Ni 2 O 7 presents the groundbreaking confirmation that high-Tc T c superconductivity is a property of strongly correlated materials beyond cuprates. We use density functional theory calculations of the band structure of La3Ni2O7 3 Ni 2 O 7 under pressure to verify that the low-energy bands are composed almost exclusively of Ni 3dx2-y2 d x 2 - y 2 and O 2p p orbitals. We deduce that the Ni 3dz2 d z 2 orbitals are essentially decoupled by the geometry of the high-pressure structure and by the effect of the Ni Hund coupling being strongly suppressed, which results from the enhanced interlayer antiferromagnetic interaction between 3dz2 d z 2 orbitals and the strong intralayer hybridization of the 3dx2-y2 d x 2 - y 2 orbitals with O 2p. p . By introducing a tight-binding model for the Fermi surfaces and low-energy dispersions, we arrive at a bilayer t- t perpendicular to- J model with strong interlayer hopping, which we show is a framework unifying La3Ni2O7 3 Ni 2 O 7 with cuprate materials possessing similar band structures, particularly the compounds La2CaCu2O6, 2 CaCu 2 O 6 , Pb2Sr2YCu3O8, 2 Sr 2 YCu 3 O 8 , and EuSr2Cu2NbO8. 2 Cu 2 NbO 8 . We use a renormalized mean-field theory to show that these systems should have (d d + is )-wave superconductivity, with a dominant d-wave component and the high Tc c driven by the near-optimally doped 9 band, while the alpha band adds an s-wave component that should lead to clear experimental signatures.