Structural health monitoring (SHM) entails the use of structural response data to identify the existence, location, and severity of structural damage. However, damage detection is a challenging problem because damage is a local phenomenon difficult to observe using global measures of structural response. With the existence and location of damage unknown a priori, sensor strategies monitoring the structure at the component-level would require dense arrays of sensors. Alternatively, this study proposes a sensing skin that can be applied to structural surfaces to monitor the strain response of the structure and the evolution of cracks. A multilayered single wall carbon nanotube-polyelectrolyte composite thin film is proposed as a sensing skin because it is piezoresistive and can be adsorbed to metallic surfaces. Electrical impedance tomography (E1T) is used to reconstruct the distribution of the sensing skin conductivity using voltage measurements taken on the boundary of the skin when regulated electrical currents are applied. The method is capable of imaging cracks in cementitious elements in addition to impact damage in aluminum plates.