The occurrence of a new type of optical phonon modes usually referred to as interface modes is one of the most interesting new characteristics of semiconductor superlattices. For superlattices consisting of polar materials they are analogues of the surface modes of thin, isolated ionic slabs discussed already by Fuchs and Kliewer [1]. Raman scattering measurements in GaAs-GaA1As superlattices [2,3] have detailed proved the existence of such excitations, reflecting directly the arrangement of the interfaces. In the framework of a strict macroscopic continuum model [4,5,6] which neglects the bulk branch dispersion confined modes occur besides the interface phonons. Both types of phonons are well separated by different properties. A careful comparison [7,8] with a parallel microscopic theory, however, shows that there should be optical phonons which simultaneously carry interface and confined character. To study this effect in more detail we develop for phonons from the centre of the superlattice Brillouin zone a lattice-dynamical theory within the continuum model but including the full dispersion of the underlying bulk phonon branches. As an example we consider a (GaAs)N~ (AlAs)N2(001) superlattice including two different lattice-matched materials GaAs (b = 1) and AlAs (b = 2) with thicknesses db= Nbao/2 (aolattice constant) and elastic force constants fb within a superlattice elementary cell. The cations (a = 1) and anions (a = 2) are characterized by their mass Mab and the ion charge +e* assumed to be material-independent. Then, starting from the microscopic equations [8], for phonons from the branch j, with eigenfrequency ~j(0), and propagating in the direction gq = sin 0~'~ + sin Og~ under an angle 0 with the growth axis g~, the equations of motion for the atomic displacements u~bj,(z, 0) can be written in the form (a,a' = 1,2;a # a';a = x,y,z;O < z < d l+d2)