Hurricanes significantly affect coastal communities, causing substantial disruption to their socio-economic systems. Therefore, post-hurricane rapid assessment is essential for effective disaster response and recovery. Traditional human-based assessments through field reconnaissance are time-consuming, leading to delays in critical decision-making. Therefore, machine learning and deep learning have emerged as powerful alternatives enabling automated, near-real-time damage evaluation. By leveraging data from past expert-classified and systematically organized events, new models can predict damage either immediately after or even during a hurricane event. This study introduces a probabilistic deep learning regression framework that predicts component-level building damage percentages using multi-view geo-coded post-disaster imagery. Unlike conventional classification models, the proposed approach estimates continuous damage ratios for eight key envelope components, enabling more detailed and loss-relevant characterization of structural damage. A pretrained convolutional backbone is integrated with a regression head to fuse features extracted from multiple building views, while a systematic hyperparameter sensitivity analysis is performed to optimize model performance. To enhance the reliability of the developed model, uncertainty quantification was incorporated using Monte Carlo dropout and bootstrapping techniques, producing confidence intervals for each prediction. Post-disaster images from Hurricane Harvey (2017), covering 436 buildings, were used as a case study to build this model. Results demonstrate that the distribution of training data strongly influences prediction accuracy across components. Both uncertainty quantification methods performed well in capturing mean values, though they diverged in their confidence intervals. Bootstrapping offered superior uncertainty characterization, albeit with a higher computational cost compared to the Monte Carlo approach.