Agents represent one of the most emerging applications of Large Language Models (LLMs) and Generative AI, with their effectiveness hinging on multimodal capabilities to navigate complex user environments. Conversational Health Agents (CHAs), a prime example of this, are redefining healthcare by offering nuanced support that transcends textual analysis to incorporate emotional intelligence. This paper introduces an LLM-based CHA engineered for rich, multimodal dialogue-especially in the realm of mental health support. It adeptly interprets and responds to users' emotional states by analyzing multimodal cues, thus delivering contextually aware and empathetically resonant verbal responses. Our implementation leverages the versatile openCHA framework, and our comprehensive evaluation involves neutral prompts expressed in diverse emotional tones: sadness, anger, and joy. We evaluate the consistency and repeatability of the planning capability of the proposed CHA. Furthermore, human evaluators critique the CHA's empathic delivery, with findings revealing a striking concordance between the CHA's outputs and evaluators' assessments. These results affirm the indispensable role of vocal (soon multimodal) emotion recognition in strengthening the empathetic connection built by CHAs, cementing their place at the forefront of interactive, compassionate digital health solutions.