Nonadiabatic molecular dynamics provides mechanistic insight into light-driven processes and informs the design of molecules and materials for solar energy conversion, photocatalysis and photo switching. Accurately describing these processes requires a representation that respects electronic symmetry and consistently relates energies to interstate couplings. Here we introduce PEACE, which combines a parity-equivariant latent Hamiltonian with a learned electronic connection. Controlled ablations reveal the complementary roles of symmetry-allowed state mixing and electronic-frame variation in reproducing crossing structures and relaxation dynamics. PEACE closely reproduces excited-state population dynamics from first-principles simulations, while its extension to spin-orbit coupling enables simulations of intersystem crossing. These results demonstrate that a more complete incorporation of the underlying physics into learned electronic representations leads to more accurate predictions of nonadiabatic dynamics.