This paper describes an ab Initio study on interface energies, misfit strain energies, and electron structures at coherent interfaces Fe(bcc structure)/MCs(NaCl structure M=Ti, Zr, Hf). The interface energies at relaxed interfaces Fe/TiC, Fe/ZrC and Fe/HfC were 0.263, 0.153 and $0.271 J/m^2$, respectively. It was understood that the dependence of interface energy on the type of carbide was closely related to changes of the binding energies between Fe, M and C atoms before and after formation of the interfaces Fe/MCs with the help of the DLP/NNBB (Discrete Lattice Plane/ Nearest Neighbour Broken Bond) model and data of the electron structures. The misfit strain energies in Fe/TiC, Fe/ZrC and Fe/HfC systems were 0.390, 1.692 and 1.408 eV per 16 atoms(Fe: 8 atoms and MC; 8 atoms). More misfit energy was generated as difference of lattice parameters between the bulk Fe and the bulk MCs increased.