The direct simultaneous acquisition of coherent imaging and strain information is of particular importance in the biomechanical characterization of biological tissue. This type of simultaneous information acquisition can be accomplished using a coupled photorefractive holography and shearography system for imaging and strain measurements, respectively. Optical scattering in a conventional speckle shearing interferometer rapidly reduces the contrast of the shearing fringes, thereby limiting the use of such interferometers with opaque surfaces. By coupling photorefractive holography with speckle shearing interferometry, properties of the photorefractive effect (spatial high-pass filtering and temporal low-pass filtering) combine to restore the shearing fringe contrast and enable strain imaging in diffusing media. This effect is demonstrated using synthetic scattering phantoms built from suspensions of silica spheres in water.