The core-level photoelectron spectra of N₂ molecules are observed at high energy resolution, resolving the 1σ_g and 1σ_u components as well as the vibrational components in the extended energy region from the threshold up to 1 keV. The σ_g/σ_u cross section ratios display modulation as a function of photoelectron momentum due to the two-centre interference, analogous to the classical Young's double-slit experiment, as predicted by Cohen and Fano a long time ago. The Cohen–Fano interference modulations display different phases depending on the vibrational excitations in the core-ionized state. Extensive ab initio calculations have been performed within the Hartree–Fock and random phase approximations in prolate spheroidal coordinates. The dependence of photoionization amplitudes on the vibrational states was taken into account using the Born–Oppenheimer approximation. The ab initio results are in reasonable agreement with the experimental data. The theoretical analysis allows the modulation to be connected with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies. Deviation from the Cohen–Fano formula is found for both the experimental and the ab initio results and is attributed to electron scattering by the neighbouring atom. A new formula for the interference modulation is derived within the framework of the multiple scattering technique. It differs from the classical Cohen–Fano formula by the addition of twice the scattering phase of the photoelectron by the neighbouring atom. We demonstrate that one can measure directly the scattering phase by fitting our formula to the experimental results.