The protection of copyrights of digital images authors is one of the most important tasks set before watermarking. What is especially important is to ensure the high robustness of a watermarked images against attacks, preventing the reading of additional information about the author. In addition, the used processing of the original image must be absolutely invisible. The presented algorithm embeds information in a parallel way-independently of the luminance and chrominance matrices in the spatial and frequency domains. The main factor motivating the use of a parallel watermark embedding via the proposed way was the mutual complementing of robustness, offered by processing in spatial and frequency domains. Additional information is recovered in a 2D cepstrum domain and in coefficients of the cosine transform. The article shows a description of a mathematical model, tests of invisibility, effectiveness and the robustness of the method were carried out. The robustness of the algorithm was shown against the following attacks: JPEG and JPEG2000 lossy compression, noise, median filtering, Low-Pass and High-Pass filtering, desynchronization, simple and inverse D/A conversion, majority cropping, photomontage and affine transforms-rotation, scaling, shearing, translation.