Foundation models pre-trained through masked reconstruction on large-scale EEG data have emerged as a promising paradigm for learning generalizable neural representations across diverse brain-computer interface applications. However, a critical yet overlooked challenge is that EEG encoders must learn representations invariant to incomplete observations-when different masked views of the same signal have minimal overlap, existing methods fail to constrain them to a consistent latent subspace, leading to degraded transferability. To address this, we propose DARE-EEG, a self-supervised foundation model that explicitly enforces the mask-invariance property through dual-aligned representation learning during pre-training. Specifically, we introduce mask alignment that constrains representations from multiple masked views of the same EEG sample via contrastive learning, complementing anchor alignment that aligns masked representations to momentum-updated complete features for semantic stability. Additionally, we propose conv-linear-probing, a parameter-efficient strategy that adapts pre-trained representations to heterogeneous electrode configurations and sampling rates through decoupled spectro-spatial projections. Extensive experiments across diverse EEG benchmarks demonstrate that DARE-EEG consistently achieves state-of-the-art in accuracy performance while maintaining relatively low parameter complexity and superior cross-dataset portability compared to existing methods. Furthermore, DARE-EEG contributes to effectively discovering and utilizing the rich potential representations in EEG.