Hyperscanning with functional near-infrared spectroscopy (fNIRS) is an emerging neuroimaging application that measures the nuanced neural signatures underlying social interactions. Researchers have assessed the effect of sex and task type (e.g., cooperation versus competition) on inter-brain coherence during human-to-human interactions. However, no work has yet used deep learning-based approaches to extract insights into sex and task-based differences in an fNIRS hyperscanning context. This work proposes a convolutional neural network-based approach to dyadic sex composition and task classification for an extensive hyperscanning dataset with $N = 222$ participants. Inter-brain signal similarity computed using dynamic time warping is used as the input data. The proposed approach achieves a maximum classification accuracy of greater than $80$ percent, thereby providing a new avenue for exploring and understanding complex brain behavior.