Accurate delineation of geologic facies and determination of live fluids from seismic reflection data is crucial for reservoir characterization during petroleum exploration. Facies classification or fluid identification is often done manually by an experienced interpreter, which makes this process subjective, laborious, and time-consuming. Several machine-learning models have been proposed to automate multiclass facies segmentation, but significant practical challenges (e.g., limited scope of labels for training purposes, skewed data distribution, inefficient performance evaluation metrics, etc) still remain. We present supervised and semisupervised Bayesian deep-learning methodologies to improve analysis of seismic facies depending on the scope of the labeled data. The developed networks reliably predict facies distribution using seismic reflection data and estimate the corresponding uncertainty. Therefore, they provide more consistent and meaningful information for seismic interpretation than commonly used deterministic approaches. We apply the proposed deep-learning models to field data from the North Sea to demonstrate the generalized-prediction capabilities of our methodology. In the case of sufficient availability of manually interpreted labels (or facies), the supervised learning model accurately recovers the facies distribution. When the amount of the interpreted labels is limited, we efficiently apply the semisupervised algorithm to avoid overfitting.