We propose a new representation learning solution for the classification of cognitive load based on Electroencephalogram (EEG). Our method integrates both time and frequency domains by first passing the raw EEG signals through the convolutional encoder to obtain the time domain representations. Next, we measure the Power Spectral Density (PSD) for all five EEG frequency bands and generate the channel power values as 2D images referred to as multi-spectral topography maps. These multi-spectral topography maps are then fed to a separate encoder to obtain the representations in frequency domain. Our solution employs a multi-domain attention module that maps these domain-specific embeddings onto a shared embedding space to emphasize more on important inter-domain relationships to enhance the representations for cognitive load classification. Additionally, we incorporate an orthogonal projection constraint during the training of our method to effectively increase the inter-class distances while improving intra-class clustering. This enhancement allows efficient discrimination between different cognitive states and aids in better grouping of similar states within the feature space. We validate the effectiveness of our model through extensive experiments on two public EEG datasets, CL-Drive and CLARE for cognitive load classification. Our results demonstrate the superiority of our multi-domain approach over the traditional single-domain techniques. Moreover, we conduct ablation and sensitivity analyses to assess the impact of various components of our method. Finally, robustness experiments on different amounts of added noise demonstrate the stability of our method compared to other state-of-the-art solutions.