We study the longwave dynamics of two-layer Couette flow with high viscosity ratio by rigorously deriving a depth-averaged integral momentum equation for the internal flow dynamics beyond criticality and a modified Kuramoto-Sivashinsky (mKS) equation for near-critical longwave interfacial dynamics. For large viscosity stratification, the primary long-wave instability is triggered by an inertia-delayed lubrication pressure that is generated when the waves introduce a Poiseuille component to the flat-him Couette flow. These primary waves can then undergo secondary modulation,due to a coupling between nonlinear wave dispersion and mean-flow gradient, to form longer waves. The secondary modulation only occurs if the plate speed exceeds a critical value that scales as (l - l(c))(-1/4) near criticality where l is the thickness of the less viscous inner fluid and l(c) is the critical thickness for the onset of the primary waves. Both primary and secondary wave transition scenarios are favorably compared to experimental data.