Radar has been widely applied in many scenarios as a critical remote sensing tool for non-contact vital sign monitoring, particularly for sleep monitoring and heart rate measurement within the home environment. For non-contact monitoring with radar, interference from house pets is an important issue that has been neglected in the past. Many animals have respiratory frequencies similar to those of humans, and they are easily mistaken for human targets in non-contact monitoring, which would trigger a false alarm because of incorrect physiological parameters from the animal. In this study, humans and common pets in families, such as dogs, cats, and rabbits, were detected using an impulse radio ultrawideband (IR-UWB) radar, and the echo signals were analyzed in the time and frequency domains. Subsequently, based on the distinct in-body structure between humans and animals, we propose a parameter, the respiratory and heartbeat energy ratio (RHER), which reflects the contribution rate of breathing and heartbeat in the detected vital signs. Combining this parameter with the energy index, we developed a novel scheme to distinguish between humans and animals. In the developed scheme, after background noise removal and direct-current component suppression, an energy indicator is used to initially identify the target. The signal is then decomposed using a variational mode decomposition algorithm, and the variational intrinsic mode functions that represent human respiration and heartbeat components are obtained and utilized to calculate the RHER parameter. Finally, the RHER index is applied to rapidly distinguish between humans and animals. Our experimental results demonstrate that the proposed approach more effectively distinguishes between humans and animals in terms of monitoring vital signs than the existing methods. Furthermore, its rapidity and need for only minimal calculation resources enable it to meet the needs of real-time monitoring.