An independent ethical assessment of an artificial intelligence system is an impartial examination of the systems development, deployment, and use in alignment with ethical values. System-level qualitative frameworks that describe high-level requirements and component-level quantitative metrics that measure individual ethical dimensions have been developed over the past few years. However, there exists a gap between the two, which hinders the execution of independent ethical assessments in practice. This study bridges this gap and designs a holistic independent ethical assessment process for a text classification model with a special focus on the task of hate speech detection. The assessment is further augmented with protected attributes mining and counterfactual-based analysis to enhance bias assessment. It covers assessments of technical performance, data bias, embedding bias, classification bias, and interpretability. The proposed process is demonstrated through an assessment of a deep hate speech detection model.