With the increasing interest for holography in 3D imaging applications, the use of hologram compression techniques is mandatory for storage and transmission purposes. The state-of-the-art approach aims at encoding separately each interference pattern by resorting to common still image compression techniques. Contrary to such an independent scheme, a novel joint hologram coding scheme is investigated in this paper. More precisely, instead of encoding all the interference patterns, it is proposed to compress only two sets of data, by taking into account the redundancies existing among them. The resulting data are encoded by applying a joint multiscale decomposition based on the vector lifting concept. Experimental results show the benefits which can be drawn from the proposed hologram compression approach.