Existing deep learning methods in multimode fiber (MMF) imaging often focus on simpler datasets, limiting their applicability to complex, real-world imaging tasks. These models are typically data-intensive, a challenge that becomes more pronounced when dealing with diverse and complex images. In this work, we propose HistoSpeckle-Net, a deep learning architecture designed to reconstruct structurally rich medical images from MMF speckles. To build a clinically relevant dataset, we develop an optical setup that couples laser light through a spatial light modulator (SLM) into an MMF, capturing output speckle patterns corresponding to input OrganAMNIST images. Unlike previous MMF imaging approaches, which have not considered the underlying statistics of speckles and reconstructed images, we introduce a distribution-aware learning strategy. We employ a histogram-based mutual information loss to enhance model robustness and reduce reliance on large datasets. Our model includes a histogram computation unit that estimates smooth marginal and joint histograms for calculating mutual information loss. It also incorporates a unique Three-Scale Feature Refinement Module, which leads to multiscale Structural Similarity Index Measure (SSIM) loss computation. Together, these two loss functions enhance both the structural fidelity and statistical alignment of the reconstructed images. Our experiments on the complex OrganAMNIST dataset demonstrate that HistoSpeckle-Net achieves higher fidelity than baseline models such as U-Net and Pix2Pix. It gives superior performance even with limited training samples and across varying fiber bending conditions. By effectively reconstructing complex anatomical features with reduced data and under fiber perturbations, HistoSpeckle-Net brings MMF imaging closer to practical deployment in real-world clinical environments.