The production of dijets with a leading neutron in ep-interactions at HERA is calculated in leading order and next-to-leading order of perturbative QCD using a pion-exchange model. Differential cross sections for deep-inelastic scattering (DIS) and photoproduction are presented as a function of several kinematic variables. By comparing the theoretical predictions for DIS dijets to recent H1 data, the pion flux factor together with the parton distribution functions of the pion is determined. The dijet cross sections in photoproduction show factorization breaking if compared to the H1 photoproduction data. The suppression factor is S = 0.48 (0.64) for resolved (global) suppression.