A high-Reynolds-number asymptotic theory is developed for linear insta
bility waves in a two-dimensional incompressible boundary layer on a f
lat surface coated with a thin film of a different fluid. The focus in
this study is on the influence of the film flow on the lower-branch T
ollmien-Schlighting waves, and also on the effect of boundary-layer/po
tential flow interaction on interfacial instabilities. Accordingly, th
e film thickness is assumed to be comparable to the thickness of a vis
cous sublayer in a three-tier asymptotic structure of lower-branch Tol
lmien-Schlichting disturbances. A fully nonlinear viscous/inviscid int
eraction formulation is derived, and computational and analytical solu
tions for small disturbances are obtained for both Tollmien-Schlichtin
g and interfacial instabilities for a range of density and viscosity r
atios of the fluids, and for various values of the surface tension coe
fficient and the Froude number. It is shown that the interfacial insta
bility contains the fastest growing modes and an upper-branch neutral
point within the chosen flow regime if the film viscosity is greater t
han the viscosity of the ambient fluid. For a less viscous film the th
eory predicts a lower neutral branch of shorter-scale interfacial wave
s. The film flow is found to have a strong effect on the Tollmien-Schl
ichting instability, the most dramatic outcome being a powerful destab
ilization of the flow due to a linear resonance between growing Tollmi
en-Schlichting and decaying capillary modes. Increased film viscosity
also destabilizes Tollmien-Schlichting disturbances, with the maximum
growth rate shifted towards shorter waves. Qualitative and quantitativ
e comparisons are made with experimental observations by Ludwieg & Hor
nung (1989).