Fine classification of city-scale buildings using satellite imagery is a crucial research area with significant implications for urban planning, infrastructure development, and population distribution analysis. However, the task faces great challenges due to low-resolution overhead images acquired from high-altitude space-borne platforms and the long-tailed sample distribution of fine-grained urban building categories, leading to a severe class imbalance problem. To address these issues, we propose a deep network approach to the fine-grained classification of urban buildings using open-access satellite images. A Denoising Diffusion Probabilistic Model (DDPM) based super-resolution method is first introduced to enhance the spatial resolution of satellite images, which benefits from domain-adaptive knowledge distillation. Then, a new fine-grained classification network with Category Information Balancing Module (CIBM) and Contrastive Supervision (CS) technique is proposed to mitigate the problem of class imbalance and improve the classification robustness and accuracy. Experiments on Hong Kong data set with 11 distinct building types revealed promising classification results with a mean Top-1 accuracy of 60.45%, which is on par with street-view image based approaches. A comprehensive ablation study demonstrates that the CIBM and CS modules improve Top-1 accuracy by 2.6% and 3.5%, respectively, over the baseline approach. In addition, these modules can be easily integrated into other classification networks, achieving similar performance improvements. This research advances urban analysis by providing an effective solution for detailed classification of buildings in complex mega-city environments using only open-access satellite imagery. The proposed technique can serve as a valuable tool for urban planners, aiding in the understanding of economic, industrial, and population distribution within cities and regions, ultimately facilitating informed decision-making in urban development and infrastructure planning. Data and code will be publicly available at https://github.com/ZhiyiHe1997/UB-FineNet.