Magnetized gas layers in gravitational fields (e.g., accretion disks and galactic disks) can be subject to the Parker instability, an undular mode of the magnetic buoyancy instabilities. By means of a linear stability analysis, we examined the effects of hot, tenuous regions (``coronae'') on the growth of the Parker instability in the underlying magnetized gas layers. As an unperturbed state, we consider the magnetized gas layers in static equilibrium. The stratified gas layers are threaded by horizontal magnetic fields in the x-direction. The temperature varies almost discontinuously at the coronal base in the z-direction. The ratio of magnetic pressure to gas pressure, α, is assumed to be constant. Our analysis has confirmed that the presence of a corona reduces the growth rate of the Parker instability and increases the critical wavelength. It is found that the growth of the Parker instability is more sensitive to the height of the coronal base than the temperature ratio between the disk and the corona is. In particular, the Parker instability is stabilized substantially when the coronal base lies below the height of maximum gravitational acceleration. When the wavenumber vector of the perturbation is parallel to the magnetic field (ky = 0), the growth rates of all modes in the disk are reduced considerably in the limit of the vanishing coronal base height. The first harmonic mode (1h-mode with odd symmetric velocity eigenfunctions with respect to the equatorial plane) is more easily stabilized by coronae than the fundamental mode is (f-mode with even symmetric velocity eigenfunctions). This is because global convective motion across the equatorial plane is allowed for the f-mode even when ky = 0, whereas it is not allowed for the 1h-mode. For the f-mode, furthermore, we find that the smallest possible γ (critical gamma) against the instability is γcrit = 1 + α, regardless of the value of ky. The reason for this is discussed briefly.