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Employing the transfer matrix method, we investigate the property of the interface optical-phonon modes (IOPMs) in a finite superlattice with a cap layer and a structural defect layer in the dielectric continuum approximation. In the present structure, there exist two types of defect IOPMs: localized modes and surface modes. The evolution of extended, localized and surface IOPMs can be clearly tracked with the thickness of the defect or cap layer. In some cases, degeneracy between surface IOPMs may occur, but the conservation of the total number of the IOPMs is always kept for every value of the transversal wave number. These results show that the spectra of these localized or surface IOPMs can be engineered by adjusting structural parameters.