An ab initio based approach to determine energies and structures for semicoherent interfaces is developed and applied to the Fe(001)/VN(001) system. To account for elastic displacements resulting from the lattice misfit, we compare an atomistic approach using a model potential (embedded-atom method) with a continuum approach using the Peierls-Nabarro model. The total interface energy of the atomistic modeling is found to be well reproduced by the Peierls-Nabarro model, demonstrating that accurate interface energies of semicoherent interfaces can be obtained by combining first principles for the chemical part of the energy and a Peierls-Nabarro model to account for the elasticity of the media.