Structural and functional brain abnormalities have been widely identified in dementia, but with variable replicability and significant overlap. Alzheimer's disease (AD) and Binswanger's disease (BD) share similar symptoms and common brain changes that can confound diagnosis. In this study, we aimed to investigate correlated structural and functional brain changes in AD and BD by combining resting-state functional magnetic resonance imaging (fMRI) and diffusion MRI. A group independent component analysis was first performed on the fMRI data to extract 49 intrinsic connectivity networks (ICNs). Then we conducted a multi-set canonical correlation analysis on three features, functional network connectivity (FNC) between ICNs, fractional anisotropy (FA) and mean diffusivity (MD). Two inter-correlated components show significant group differences. The first component demonstrates distinct brain changes between AD and BD. AD shows increased cerebellar FNC but decreased thalamic and hippocampal FNC. Such FNC alterations are linked to the decreased corpus callosum FA. AD also has increased MD in the frontal and temporal cortex, but BD shows opposite alterations. The second component demonstrates specific brain changes in BD. Increased FNC is mainly between default mode and sensory regions, while decreased FNC is mainly within the default mode domain and related to auditory regions. The FNC changes are associated with FA changes in posterior/middle cingulum cortex and visual cortex and increased MD in thalamus and hippocampus. Our findings provide evidence of linked functional and structural deficits in dementia and suggest that AD and BD have both common and distinct changes in white matter integrity and functional connectivity.