Negative ion photoelectron spectroscopy was used to elucidate the electronic and geometric structure of the gaseous Al2N/Al2N- molecules, using photodetachment wavelengths of 416 nm (2.977 eV), 355 nm (3.493 eV), and 266 nm (4.661 eV). Three electronic bands are observed and assigned to the X-2 Sigma(+)(u) <- X-1 Sigma(+)(g), A(2)Pi(u) <- X-1 Sigma(+)(g), and B-2 Sigma(+)(g) <- X-1 Sigma(+)(9) electronic transitions, with the caveat that one or both excited states may be slightly bent. With the aid of density functional theory calculations and Franck-Condon spectral simulations, we determine the adiabatic electron affinity of Al2N, 2.571 +/- 0.008 eV, along with geometry changes upon photodetachment, vibrational frequencies, and excited-state term energies. Observation of excitation of the odd vibrational levels of the antisymmetric stretch (v(3)) suggests a breakdown of the Franck-Condon approximation, caused by the vibronic coupling between the X2Xu+ and B-2 Sigma(+)(g) electronic states through the v(3) mode.