Due to the dynamic health status of patients and discrepant stability of physiological variables, health data often presents as irregular multi-rate multivariate time series (IMR-MTS) with significantly varying sampling rates. Existing methods mainly study changes of IMR-MTS values in the time domain, without considering their different dominant frequencies and varying data quality. Hence, we propose a novel Cooperative Joint Attentive Network (CJANet) to analyze IMR-MTS in frequency domain, which adaptively handling discrepant dominant frequencies while tackling diverse data qualities caused by irregular sampling. In particular, novel dual-channel joint attention is designed to jointly identify important magnitude and phase signals while detecting their dominant frequencies, automatically enlarging the positive influence of key variables and frequencies. Furthermore, a new cooperative learning module is introduced to enhance information exchange between magnitude and phase channels, effectively integrating global signals to optimize the network. A frequency-aware fusion strategy is finally designed to aggregate the learned features. Extensive experimental results on real-world medical datasets indicate that CJANet significantly outperforms existing methods and provides highly interpretable results.