Deep learning (DL) methods recently show promise on accurate brain disorder classification using functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI). However, DL model building can be hindered by small sample-size settings of fMRI. Moreover, most studies utilize either static (sFC) or dynamic FC (dFC) for classification. We propose a unified framework for data augmentation of both sFC and dFC for multi-domain joint classification of brain disorders. We exploit generative adversarial networks (GAN) to synthesize realistic FCs for data augmentation. Notably, we adopted the TimeGAN for dFC generation that can capture temporal dependencies in real dFC, and the GR-SPD-GAN for sFC generation that preserves the spatial connectivity structure. We further develop BrainFusionNet - a specialized DL model for multi-domain FC that simultaneously learns embedded features from both sFC and dFC to provide complementary spatio-temporal information for downstream classification. The synthetic FC data are augmented in training data to improve the BrainFusionNet performance and generalizability. Experimental results on major depressive disorder (MDD) identification using resting-state fMRI show substantial improvement in classification accuracy by our framework, outperforming competing models without FC augmentation and using sFC or dFC features alone.