The coherent interface energies and misfit strain energies of Fe/XN (X=Ti, Zr, Hf) systems were calculated by first principles method. The interface energies in Fe/TiN, Fe/ZrN and Fe/HfN systems were 0.343, 0.114, and 0.030 $J/m^2$, respectively. Influence of bond energy was estimated using the discrete lattice plane/nearest neighbor broken bond(DLP/NNBB) model. It was found that the dependence of interface energy on the type of nitride was closely related to changes of the bond energies between Fe, X and N atoms before and after formation of the Fe/XN interfaces. The misfit strain energies in Fe/TiN, Fe/ZrN, and Fe/HfN systems were 0.239, 1.229, and 0.955 eV per 16 atoms(Fe; 8 atoms and XN; 8 atoms). More misfit strain energy was generated as the difference of lattice parameters between the bulk Fe and the bulk XNs increased.