Dispersion equations of hydromagnetic oscillations in the magnetopause-magnetosheath region are derived in the two-fluid approximation with the ion temperature higher than the electron temperature. In the derivation a finite thickness of the magnetosheath and the presence of the main ion drift motion in the magnetosphere are taken into account, in addition to the tangential uniform flow in the magnetosheath. It is shown that there are two different kinds of oscillations in the region, which are in general coupled to each other. One is radial oscillations related to the nonuniform compressed flow in the magnetosheath and the other is the Kelvin-Helmholtz instability of boundary waves due to the tangential flow. The fundamental mode of the former oscillation, taking a maximum displacement at the magnetopause, has an eigen period of 8 minutes, which is comparable with that of the observed oscillations obtained by particle data of ISEE 1 and 2 satellites. For a range of the tangential wavelength shorter than the thickness of the magnetosheath, dominant eigen oscillations are the boundary waves. The finite thickness has a tendency to reduce the boundary wave instability. The predicted relative phase differences between orientation angle and radial velocity of the moving magnetopause for the marginal state of oscillations are in phase in the morning and out of phase in the afternoon.