Laser directed energy deposition (DED) additive manufacturing struggles with consistent part quality due to complex melt pool dynamics and process variations. While much research targets defect detection, little work has validated process monitoring systems for evaluating melt pool dynamics and process quality. This study presents a novel multimodal monitoring framework, synergistically integrating contact-based acoustic emission (AE) sensing with coaxial camera vision to enable layer-wise identification and evaluation of geometric variations in DED parts. The experimental study used three part configurations: a baseline part without holes, a part with a 3mm diameter through-hole, and one with a 5mm through-hole to test the system's discerning capabilities. Raw sensor data was preprocessed: acoustic signals were filtered for time-domain and frequency-domain feature extraction, while camera data underwent melt pool segmentation and morphological feature extraction. Multiple machine learning algorithms (including SVM, random forest, and XGBoost) were evaluated to find the optimal model for classifying layer-wise geometric variations. The integrated multimodal strategy achieved a superior classification performance of 94.4%, compared to 87.8% for AE only and 86.7% for the camera only. Validation confirmed the integrated system effectively captures both structural vibration signatures and surface morphological changes tied to the geometric variations. While this study focuses on specific geometries, the demonstrated capability to discriminate between features establishes a technical foundation for future applications in characterizing part variations like geometric inaccuracies and manufacturing-induced defects.