To develop intelligent speech assistants and integrate them seamlessly with intra-operative decision-support frameworks, accurate and efficient surgical phase recognition is a prerequisite. In this study, we propose a multimodal framework based on Gated Multimodal Units (GMU) and Multi-Stage Temporal Convolutional Networks (MS-TCN) to recognize surgical phases of port-catheter placement operations. Our method merges speech and image models and uses them separately in different surgical phases. Based on the evaluation of 28 operations, we report a frame-wise accuracy of 92.65 $\pm$ 3.52% and an F1-score of 92.30 $\pm$ 3.82%. Our results show approximately 10% improvement in both metrics over previous work and validate the effectiveness of integrating multimodal data for the surgical phase recognition task. We further investigate the contribution of individual data channels by comparing mono-modal models with multimodal models.