Melanoma skin disease is a major concern for skin cancer-related deaths worldwide. Early diagnosis and detection are crucial for improving patient outcomes. However, existing detection methods often result in false alarms, highlighting the need for more accurate and reliable approaches. This paper proposes a Dual-Stream Semi-Supervised Melanoma Network (DS-MelNet) for melanoma detection. The DS-MelNet utilizes a semi-supervised learning framework to incorporate both labeled and unlabeled data, enhancing detection accuracy. The model's performance is evaluated on the SIIM-ISIC Melanoma Classification Challenge dataset. The dataset undergoes hair detection and removal from skin lesion images using three algorithms proposed in literature viz. Modified Dull Razor, Modified E-shaver and Adaptive principle curvature with Modified dull razor fusion. Performance of the proposed models is assessed through commonly used metrics that include Accuracy, Recall, Precision, and F1-score. Comparative analysis of the DS-MelNet is performed against two benchmarks: Simple Convolutional Neural Network (SCNN) and a Fine-tuned VGG-16 model proposed in this paper. The results clearly indicate that the DS-MelNet demonstrates superior performance, achieving an accuracy of 86% and outperforming both SCNN (76%) and VGG-16 (82%) models. This exceptional performance underscores the potential of the DS-MelNet for effective melanoma classification. The study highlights the promise of semi-supervised learning frameworks and sophisticated neural networks in enhancing melanoma diagnostics. The ability of the proposed model to learn from a small set of labeled data makes it highly suitable for real-world applications where annotated datasets are limited.