Human-robot collaboration (HRC) is a key focus of Industry 5.0, aiming to enhance worker productivity while ensuring well-being. The ability to perceive human psycho-physical states, such as stress and cognitive load, is crucial for adaptive and human-aware robotics. This paper introduces MultiPhysio-HRC, a multimodal dataset containing physiological, audio, and facial data collected during real-world HRC scenarios. The dataset includes electroencephalography (EEG), electrocardiography (ECG), electrodermal activity (EDA), respiration (RESP), electromyography (EMG), voice recordings, and facial action units. The dataset integrates controlled cognitive tasks, immersive virtual reality experiences, and industrial disassembly activities performed manually and with robotic assistance, to capture a holistic view of the participants' mental states. Rich ground truth annotations were obtained using validated psychological self-assessment questionnaires. Baseline models were evaluated for stress and cognitive load classification, demonstrating the dataset's potential for affective computing and human-aware robotics research. MultiPhysio-HRC is publicly available to support research in human-centered automation, workplace well-being, and intelligent robotic systems.