Passive wireless human sensing has attracted increasing attention due to its non-contact nature and robustness under different lighting conditions. This paper proposes a system for multiperson detection and vital-sign (i.e., respiration and heartbeat) monitoring using space-time-coding (STC) reconfigurable intelligent surfaces (RISs). Specifically, the proposed system scans the area of interest (AoI) for human detection by using the STC RIS-generated harmonic beams. Simultaneously, specific beams are assigned to the detected persons for vital-sign sensing. Furthermore, we propose an improved variational mode decomposition (VMD) algorithm to process the reflected echo signal and estimate respiration and heartbeat rates of the detected persons. We build a prototype to validate the proposed system. Experimental results demonstrate that the system can simultaneously monitor respiration and heartbeat of up to four persons, with average errors below 1 RPM (respiration per minute) and 5 BPM (beats per minute). Further analysis reveals that the flexible beam control enabled by the STC RIS can reduce the noise reflected by irrelative objects, thus improving the signal-to-noise ratio of echoes from the human chest. This work offers a contact-free care to round-the-clock monitor vital signs of multiple persons, which are critical indicators for assessing general health state and identifying various diseases.