Common factors and microcounseling skills are critical to the effectiveness of psychotherapy. Understanding and measuring these elements provides valuable insights into therapeutic processes and outcomes. However, automatic identification of these change principles from textual data remains challenging due to the nuanced and context-dependent nature of therapeutic dialogue. This paper introduces CFiCS, a hierarchical classification framework integrating graph machine learning with pretrained contextual embeddings. We represent common factors, intervention concepts, and microcounseling skills as a heterogeneous graph, where textual information from ClinicalBERT enriches each node. This structure captures both the hierarchical relationships (e.g., skill-level nodes linking to broad factors) and the semantic properties of therapeutic concepts. By leveraging graph neural networks, CFiCS learns inductive node embeddings that generalize to unseen text samples lacking explicit connections. Our results demonstrate that integrating ClinicalBERT node features and graph structure significantly improves classification performance, especially in fine-grained skill prediction. CFiCS achieves substantial gains in both micro and macro F1 scores across all tasks compared to baselines, including random forests, BERT-based multi-task models, and graph-based methods.