The discovery of superconductivity at 80 K under high pressure in La_3⁢Ni₂⁢O₇ presents the groundbreaking confirmation that high-𝑇_𝑐 superconductivity is a property of strongly correlated materials beyond cuprates. We use density functional theory calculations of the band structure of La_3⁢Ni₂⁢O₇ under pressure to verify that the low-energy bands are composed almost exclusively of Ni 3⁢𝑑_{𝑥²−𝑦²} and O 2⁢𝑝 orbitals. We deduce that the Ni 3⁢𝑑_𝑧² 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 3⁢𝑑_𝑧² orbitals and the strong intralayer hybridization of the 3⁢𝑑_{𝑥²−𝑦²} orbitals with O 2⁢𝑝. By introducing a tight-binding model for the Fermi surfaces and low-energy dispersions, we arrive at a bilayer 𝑡−𝑡_⊥−𝐽 model with strong interlayer hopping, which we show is a framework unifying La₃⁢Ni₂⁢O₇ with cuprate materials possessing similar band structures, particularly the compounds La_2⁢CaCu_2⁢O₆, Pb₂⁢Sr₂⁢YCu_3⁢O₈, and EuSr_2⁢Cu_2⁢NbO₈. We use a renormalized mean-field theory to show that these systems should have (𝑑 + 𝑖⁢𝑠)-wave superconductivity, with a dominant 𝑑-wave component and the high 𝑇_𝑐 driven by the near-optimally doped 𝛽 band, while the 𝛼 band adds an 𝑠-wave component that should lead to clear experimental signatures.