Functional connectivity networks (FCNs) using resting-state functional magnetic resonance imaging (rs-fMRI) have been applied to the analysis and diagnosis of brain disease, such as Alzheimer's disease (AD) and its prodrome, i.e., mild cognitive impairment (MCI). Different from conventional studies focusing on static descriptions on functional connectivity (FC) between brain regions in rs-fMRI, recent studies have resorted to dynamic connectivity networks (DCNs) to characterize the dynamic changes of FC, since dynamic changes of FC may indicate changes in macroscopic neural activity patterns in cognitive and behavioral aspects. However, most of the existing studies only investigate the temporal properties of DCNs (e.g., temporal variability of FC between specific brain regions), ignoring the important spatial properties of the network (e.g., spatial variability of FC associated with a specific brain region). Also, emerging evidence on FCNs has suggested that, besides temporal variability, there is significant spatial variability of activity foci over time. Hence, integrating both temporal and spatial properties of DCNs can intuitively promote the performance of connectivity-network-based learning methods. In this paper, we first define a new measure to characterize the spatial variability of DCNs, and then propose a novel learning framework to integrate both temporal and spatial variabilities of DCNs for automatic brain disease diagnosis. Specifically, we first construct DCNs from the rs-fMRI time series at successive non-overlapping time windows. Then, we characterize the spatial variability of a specific brain region by computing the correlation of functional sequences (i.e., the changing profile of FC between a pair of brain regions within all time windows) associated with this region. Furthermore, we extract both temporal variabilities and spatial variabilities from DCNs as features, and integrate them for classification by using manifold regularized multi-task feature learning and multi-kernel learning techniques. Results on 149 subjects with baseline rs-fMRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) suggest that our method can not only improve the classification performance in comparison with state-of-the-art methods, but also provide insights into the spatio-temporal interaction patterns of brain activity and their changes in brain disorders.