We present a first-principles derivation of the joint-bath decoherencecross-coupling term introduced phenomenologically in a companion study(Paper I). Starting from a generalized Caldeira–Leggett model withmutually coupled bosonic baths, we perform a canonical transformationto mass-weighted coordinates, diagonalizing the bath Hamiltonian intoindependent normal modes. This transformation yields an explicitanalytical expression for the cross-spectral density J₁₂(ω). We showthat the Cauchy–Schwarz inequality provides a fundamental bound on thenormalized cross-correlation coefficient, ensuring |ρ(ω)| ≤ 1. Numerical validation on a minimal two-mode Ohmic–Drude model indicatesthat the phenomenological value ρ ≈ 0.855 (extracted from experimentalinterferometry data in Paper I) is consistent with a weak-to-moderateinter-bath coupling strength λ_opt ≈ 0.095, corresponding to aphysically realistic coupling ‖H_B1B2‖/‖H_Bi‖ ≲ 12%. Finally, we demonstrate that the bilinear form c·u·v used in thephenomenological model arises as the leading-order Taylor approximationof the exact microscopic √(uv) dependence around a nominal operatingpoint (u₀,v₀), consistent with physical boundary conditions. This workprovides a microscopic foundation for the empirical joint-bath modeland opens pathways for future non-Markovian and solid-state extensions. Full Changelog: 18.0-C...18.0-C-Paper