Aircraft icing is an important concern in aviation safety. Improvements in the computational models of ice accretion are an important step in improving safety in icing conditions. One of the improvements necessary for these models is a better understanding of surface water transport and its role in the ice accretion process. Changes in water mass flux can alter the shape and location of larger scale ice growth, thereby affecting the aerodynamics of the airfoil. While past analyses have assumed a Couette flow in the film and ignored surface waves, more recent research has begun to look at the effect of these interfacial waves. These studies have found that the mass flux can, in some cases, be greatly increased by these surface processes. This study examines the effect of droplet impingement on thin water films to assess any impact on overall interfacial wave structure and mass transport. The theory is first developed, without including droplet impingement, to describe the limit as water film thickness goes to zero. In this limit the air shear stress becomes the dominant driving force behind interfacial wave development, and the governing equations can be simplified to a single modified Kuramoto-Sivashinsky equation. To model the droplet impact, a backward time singularity of the film equation was found, which is expected to be consistent with vertically impacting droplets. It was found that there are realistic droplet volume and frequency combinations which result in significantly increased mass flux within the film. The results of this study also suggest that there are larger scale disturbances triggered by the droplets which require further consideration.