Bimetallic surface plasmon resonance (SPR) sensors have the potential to overcome the drawbacks of individual metals, but the effect of the configuration of the two metallic layers on the performance of the sensors has not been explored. This study examines the influence of different positions of a thin layer of silver in relation to a copper layer on the sensitivity of such a bimetallic SPR sensor. The design of this configuration aims to improve the SPR reflectance curve and strengthen the evanescent electric field to improve the sensor efficiency. Our findings indicate that, by optimizing the architectures of SPR sensors and using a silver–copper bimetallic structure, we can achieve superior performance compared to devices that utilize only silver or copper. The optimized Ag (5 nm)/Cu (55 nm) sensor design, with the best sensitivity of 299.09° RIU−1, can detect a change of 0.43°/(g dl−1) for hemoglobin in blood, 0.35°/(g dl−1) for glucose in urine, and 0.1°/(%) for methanol in ethanol. We also demonstrate the importance of signal quality by introducing two new parameters that offer a better quantitative indication of the efficiency of a sensor than is obtained by using only sensitivity.