The objective of this work is to deblur face videos. We propose a method that tackles this problem from two directions: (1) enhancing the blurry frames, and (2) treating the blurry frames as missing values and estimate them by interpolation. These approaches are complementary to each other, and their combination outperforms individual ones. We also introduce a novel module that leverages the structure of faces for finding positional offsets between video frames. This module can be integrated into the processing pipelines of both approaches, improving the quality of the final outcome. Experiments on three real and synthetically generated blurry video datasets show that our method outperforms the previous state-of-the-art methods by a large margin in terms of both quantitative and qualitative results.