The copyright protection of three-dimensional (3D) content is a matter of interest in artistic and creative works due to the rights of the holder for the distribution of the material. However, although stereo images are widely used for the generation of 3D content, there is a little amount of research focused on copyright protection for this type of image. In this study, a novel invisible and blind color image watermarking framework for protecting the copyright of the stereo images based on Binocular Just Noticeable Difference (BJND) and lower-and-upper (LU) decomposition is proposed. In this framework, a color watermark is encoded to reduce the information. Then, the BJND model is calculated in the R channel of a stereo image, and finally, LU decomposition is applied into the G and B channels to embed and extract a color watermark. The BJND model has demonstrated a remarkable sensitivity comparable with the Human Visual System (HVS) in luminance changes such as the ones presented in stereo images, guaranteeing a good protection performance and a high imperceptibility. The proposed framework was compared with other state-of-the-art techniques, and it has demonstrated better performance and high resistance to attacks of JPEG compression or impulsive and Gaussian noise. Additionally, this novel framework does not affect the generation of the disparity map or the 3D content when the watermarked stereo images are used for their creation.