Engagement between client and therapist is a critical determinant of therapeutic success. We propose a multi-dimensional natural language processing (NLP) framework that objectively classifies engagement quality in counseling sessions based on textual transcripts. Using 253 motivational interviewing transcripts (150 high-quality, 103 low-quality), we extracted 42 features across four domains: conversational dynamics, semantic similarity as topic alignment, sentiment classification, and question detection. Classifiers, including Random Forest (RF), Cat-Boost, and Support Vector Machines (SVM), were hyperparameter tuned and trained using a stratified 5-fold cross-validation and evaluated on a holdout test set. On balanced (non-augmented) data, RF achieved the highest classification accuracy (76.7%), and SVM achieved the highest AUC (85.4%). After SMOTE-Tomek augmentation, performance improved significantly: RF achieved up to 88.9% accuracy, 90.0% F1-score, and 94.6% AUC, while SVM reached 81.1% accuracy, 83.1% F1-score, and 93.6% AUC. The augmented data results reflect the potential of the framework in future larger-scale applications. Feature contribution revealed conversational dynamics and semantic similarity between clients and therapists were among the top contributors, led by words uttered by the client (mean and standard deviation). The framework was robust across the original and augmented datasets and demonstrated consistent improvements in F1 scores and recall. While currently text-based, the framework supports future multimodal extensions (e.g., vocal tone, facial affect) for more holistic assessments. This work introduces a scalable, data-driven method for evaluating engagement quality of the therapy session, offering clinicians real-time feedback to enhance the quality of both virtual and in-person therapeutic interactions.