= Solution
Use superscripts $T$ and $D$ for the thin-upper-layer and two-deep-layer cases. The cutoff is identical, while
$$
\boxed{\frac{k_m^T}{k_m^D}\sim\sqrt{\frac32},\qquad
\frac{\sigma_m^T}{\sigma_m^D}\sim\left[\frac{3\sqrt3(\rho_1+\rho_2)}{8\rho_1}\,k_cL_1\right]^{1/2}\ll1.}
$$
Thus confinement suppresses the <Rayleigh-Taylor instability> growth strongly, but moves the most amplified disturbance to a somewhat larger <wavenumber>. The cutoff depends on the gravity-capillary balance, whereas growth depends also on the inertia of the moving layers.
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