Time courses (TC)  and functional network connectivity (FNC) features, derived from functional magnetic resonance imaging, show considerable potential in the study of brain disorders. Despite significant advancements, most deep learning approaches tend to either directly concatenate complementary MRI features at the input level or ensemble decisions after separately learning each feature, whereas an end-to-end, mixed feature learning framework is still lacking. To bridge this gap, we introduce a cross-feature mutual learning (CFML)  to enable collaborative learning of TC-specific and FNC-specific models and facilitate mutual knowledge transfer to distill shared and robust characteristics from the high-level representations of TC and FNC, thereby enhancing brain disorder classification performance. Specifically, we first develop a recurrent neural network-based TC-specific encoder to capture temporal dynamic dependencies within TCs, alongside a transformer-based FNC-specific encoder to discern global high-order functional dependencies among independent components in FNCs. Subsequently, we design a cross-modal module for the adaptive integration of TC-specific and FNC-specific features. Additionally, the CFML strategy is proposed to collaboratively train these modules, incorporating feature-specific loss, feature-exchange loss, and joint loss. Empirical results reveal that CFML achieves an accuracy of 85.1% in differentiating healthy controls (HC) from schizophrenia (SZ) patients, surpassing 12 comparative models by a margin of 3.0-9.2% accuracy using either static FNC or TCs or both. These findings underscore the efficacy of CFML in classifying brain disorders, highlighting its potential in advancing this field.