An electronic device may include a display layer including light transmissive portions and non-transmissive portions. The electronic device may also include a palm biometric image sensor layer beneath the display layer and configured to sense an image of a user's palm positioned above the display layer based upon light reflected from the user's palm passing through the light transmissive portions of the display layer. The electronic device may further include a controller configured to capture image data from the user's palm in cooperation with the palm biometric image sensor layer and determine a surface distortion of the user's palm based upon the image data. The controller may also be configured to perform a biometric authentication of the user's palm based upon the image data and the surface distortion.