This work concerns the asymptotic behaviour of the eigenvalues and eigenvectors of a problem posed on an ε-periodic two-component domain with an imperfect interface. We obtain characterizations of the eigenvalues and give homogenization results using the periodic unfolding method. The eigenvalues of the ε-problem converge to the corresponding eigenvalues of the limit problem, for the whole sequence. The same convergence result is obtained for the corresponding eigenspaces. The convergence for the whole sequence of the corresponding eigenvectors is achieved when the associated homogenized eigenvalue is simple.