In this study, a stretchable polymer optical fiber with a sandwich structure was proposed, which integrated a silicone tube filled with polydimethylsiloxane (PDMS) with two common commercial polymethylmethacrylate (PMMA) optical fiber. By integrating the stretchable polymer optical fiber into the designed sleep-monitoring mattress, the pressure sensitivity of the mattress to measure human respiratory rate, heart rate, and body motion information is improved. The weak respiratory and heartbeat signals were amplified by an amplifier circuit and the respiratory and heart rates were obtained by an algorithm. The experimental results indicated that the mattress can monitor respiratory rate and heart rate values in different positions as well as body movement information and can differentiate between three different behavioral states, including not on the bed, lying, and moving on the bed. In addition, clinical trials were conducted on 10 subjects, and the results were analyzed using the Bland-Altman analysis method, confirming the accuracy of the mattress, with maximum errors of less than 1 breath per minute and 2 beats per minute for respiration and heartbeat respectively. In addition, the mattress's reliability and stability were verified through continuous sleep monitoring at various times of day. The mattress has the advantages of low cost, softness, comfort, and high sensitivity, and is suitable as a home medical device for long-term continuous monitoring of respiratory and heart rates during sleep.