Close-to-real-time mental health monitoring has gained significant interest in affective computing, particularly for emotion recognition and affective state analysis in stressful situations. Most commonly, conventional approaches use only one modality, such as speech, facial expressions, or physiological signals, and these are not always capable of capturing the complexity and dynamism of affective responses. While recent multimodal formats have achieved strong predictive performance, many remain sensitive to noisy inputs, missing modalities, insufficient modelling of cross-modal interactions, and inadequate handling of heterogeneous data. This paper proposes a multimodal deep learning framework, MentalHealthSense-AI, to overcome these challenges by combining EEG, speech and facial features for affective state analysis. The framework proposed in this work consists of modality-specific encoders and a reliability-aware cross-modal attention mechanism that adaptively adjusts the contribution of modalities based on signal quality. Moreover, a joint affective state estimation approach and a streaming inference pipeline with temporal smoothing are integrated to ensure stable, low-latency predictions. Experimental testing on benchmark datasets shows that the system has strong predictive capabilities, achieving up to 95.2% accuracy and 94.8% F1 score for emotion recognition, and a low error rate in estimating affective indicators of stress, with a minimum MSE of 0.018. Comparisons with recently developed multimodal affective computing systems also show competitive results, tolerance to noisy and missing modalities, and high cross-dataset generalisation. These results illustrate that MentalHealthSense-AI can serve as a reliable, interpretable, and flexible multimodal framework for long-term continuous affective state monitoring and real-time mental health support applications, and suggest that it has the potential for future deployment on resource-constrained and wearable computing platforms, with further optimisation and hardware-specific validation.