The laser fluorescence excitation spectrum of the AlNe complex, in the vicinity of the Al atomic 3d<--3p and 5s<--3p atomic transitions, is reported. Transitions out of the upsilon=0 vibrational levels of both lower-state spin-orbit levels, X-1 (2) Pi(1/2) and X-2 (2) Pi(3/2), to vibrational levels of the C (2) Delta, D (2) Pi, and H (2) Sigma(+) AlNe electronic states were observed. From observations of the onset of excitation to the Al(3d)+Ne dissociation continuum, dissociation energies for the various AlNe electronic states were determined. Ab initio calculations of AlNe electronic states correlating with the ground Al(3p) + Ne atomic asymptote were also carried out. The X-1 (2) Pi(1/2) and X-2 (2) Pi(3/2) binding energies computed using the calculated AlNe(X (2) Pi, A (2) Sigma(+)) potential energy curves were in reasonable agreement with the experimental determinations. The experimentally determined dissociation energy for the X-2 (2) Pi(3/2) level is significantly larger than that of the ground X-1 (2) Pi(1/2) level (D-0=32.3+/-0.3 and 14.1+/-0.3 cm(-1), respectively).