Accurate classification of cognitive states from Electroencephalographic (EEG) signals is crucial in neuroscience applications such as Brain-Computer Interfaces (BCIs). Classification pipelines based on Riemannian geometry are often state-of-the-art in the BCI field. In this type of BCI, covariance matrices based on EEG signals of independent frequency bands are used as classification features. However, there is significant neuroscience evidence of neural interactions across frequency bands, such as cross-frequency coupling (CFC). Therefore, in this paper, we propose novel symmetric positive definite (SPD) matrix representations considering CFC for Riemannian geometry-based EEG classification. The spatial interactions of phase and amplitude within and between frequency bands are described in three different CFC SPD matrices. This allows us to include additional discriminative neurophysiological features that are not available in the conventional Riemannian EEG features. Our method was evaluated using a mental workload classification task from a public passive BCI dataset. Our fused model of the three CFC covariance matrices showed statistically significant improvements in average classification accuracies from the conventional covariance matrix in the theta and alpha bands by 18.32% and in the beta and gamma bands by 4.34% with smaller standard deviations. This result confirmed the effectiveness of considering more diverse neurophysiological interactions within and between frequency bands for Riemannian EEG classification.