Cognitive impairment (CI) in multiple sclerosis (MS) is only partially explained by whole-brain volume measures, but independent component analysis (ICA) can extract regional patterns of damage in grey matter (GM) or white matter (WM) that have proven more closely associated with CI. Pathology in GM and WM occurs in parallel, and so patterns can span both. This study assessed whether joint-ICA of GM and WM features better explained cognitive function compared to single-tissue ICA. 89 people with MS underwent cognitive testing and magnetic resonance imaging. Structural T1 and diffusion-weighted images were used to measure GM volumes and WM connectomes (based on fractional anisotropy weighted by the number of streamlines). ICA was performed for each tissue type separately and as joint-ICA. For each tissue type and joint-ICA, 20 components were extracted. In stepwise linear regression models, joint-ICA components were significantly associated with all cognitive domains. Joint-ICA showed the highest variance explained for executive function (Adjusted R