Contrast-enhanced ultrasound (CEUS) allows a visualization of the vascularization and complements the anatomical information provided by conventional ultrasound (US). However, these images are inherently subject to noise and shadows, which hinders standard segmentation algorithms. In this paper, we propose to use simultaneously the different information coming from 3D US and CEUS images to address the problem of kidney segmentation. To that end, we introduce a generic framework for joint co-segmentation and registration that seeks objects having the same shape in several images. From this framework, we derive both an ellipsoid co-detection and a model-based co-segmentation algorithm. These methods rely on voxel-classification maps that we estimate using random forests in a structured way. This yields a fast and fully automated pipeline, in which an ellipsoid is first estimated to locate the kidney in both US and CEUS volumes and then deformed to segment it accurately. The proposed method outperforms state-of-the-art results (by dividing the kidney volume error by two) on a clinically representative database of 64 images.