We introduce a joint Variational Network (jVN) to reconstruct multi-contrast data jointly from accelerated MRI acquisitions. By taking advantage of the shared structural information among different clinical contrasts, jVN better preserved small anatomical features when compared to standard single-contrast VN. Combining jVN with the efficient Wave-CAIPI acquisition scheme enabled rapid 3D volumetric scans at R=16x acceleration. This approach was evaluated at 3T using in-vivo data from three clinical contrasts, resulting in up to a 54% reduction in RMSE when compared to standard Wave-CAIPI reconstructions. The jVN reconstructions preserved both high spatial resolution and good image quality.