The full interaction potential between Ne(S-1) and Ne+(P-2) is determined by least-squares fitting of potential parameters to spectroscopic data, principally from the near-dissociation microwave spectra of the Ne-2(+) complex. The potential obtained in this way incorporates the potential curves for all six electronic states correlating with Ne(S-1)+Ne+(P-2) and the couplings between them. Coupled-channel calculations on the potential take account of breakdown of the Born-Oppenheimer approximation and provide an accurate description of the microwave rovibronic spectrum involving levels within similar to10 cm(-1) of the first dissociation limit. The Ne-2(+) ions are both vibrationally and rotationally hot: the spectrum involves levels up to at least J=25/2 and there is evidence for transitions involving levels near the second dissociation limit. The long-range levels involved have up to 12 Angstrom, compared with an equilibrium bond length of 1.756 Angstrom for the ground electronic state. The long-range parameters of the interaction can be extracted from the fit and are compared with recent theoretical values.