Complex biological features such as the human microbiome and gene expressions play a crucial role in human health by mediating various biomedical processes that influence disease progression, such as immune responses and metabolic processes. Understanding these mediation roles is essential for gaining insights into disease pathogenesis and improving treatment outcomes. However, analyzing such high-dimensional mediation features presents challenges due to their inherent structural and correlations, such as the hierarchical taxonomic structures in microbial operational taxonomic units (OTUs), gene-pathway relationships, and the high dimensionality of the datasets, which complicates mediation analysis. We propose the Med-CNN model, an iterative approach using Convolutional Neural Networks (CNNs) to incorporate the complex biological network of the mediation features. The output values from network-specific CNN models are condensed into an integrative mediation metric (IMM), which captures essential biological information for estimating mediation effects. Our approach is designed to handle high-dimensional data and accommodate their unique structures and non-linear interactive mediation effects. Through comprehensive simulation studies, we evaluated the performance of our algorithm across different scenarios, including various mediation effects, effect sizes, and sample sizes, and we compared it to conventional methods. Our simulations demonstrated consistently lower biases in mediation effect estimates, with values ranging from 0.17 to 0.56, which were lower than other established methods ranging from 0.24 to 13.27. In a real data application, our method identified a mediation effect of 0.06 between ethnicity and vaginal pH levels.