The surface morphology of thin molten films of phase separating mixtures of poly(ethylenepropylene) (PEP) and perdeuterated poly(ethylenepropylene) (dPEP) of the critical composition were investigated using scanning force microscopy. Volume fraction versus depth profiles were also obtained using time-of-flight forward recoil spectrometry (TOF-FRES). The free surface of a film with a nominal thickness of about d = 200 nm is initially smooth but develops a regular roughness pattern, with a wavelength about 500 nm and an amplitude about 2.5 nm, after a certain annealing time, which corresponds to the transition from a four-layer (dPEP/PEP/dPEP/PEP) to a two-layer (dPEP/PEP) phase-separated domain structure in the direction normal to the film thickness. At much longer times the two-layer films become smooth again. We attribute these fine surface patterns to transient pressure differences accompanying mass transport by hydrodynamic flow, where this transport occurs though perforations in the PEP-rich layered domain just below the dPEP-rich surface layer. This flow is driven by the pressure beneath the highly curved lateral interfaces of the intermediate layers. In keeping with this hypothesis, thicker films (d > 280 nm), which do not develop breaks in the PEP-rich layered domain and for which diffusional transport is necessary for coarsening of the layer structure to occur, do not show this transient roughening.