Wearable electronics play important roles in noninvasive, continuous, and personalized monitoring of multiple biosignals generated by the body. To unleash their full potential for the next-generation human-centered bio-integrated electronics, wireless sensing capability is a desirable feature. However, state-of-the-art wireless sensing technologies exploit rigid and bulky electronic modules for power supply, signal generation, and data transmission. This study reports a battery-free device technology based on a "two-part" resonance circuit model with modularized, physically separated, and detachable functional units for magnetic coupling and biosensing. The resulting platform combines advantages of electronics and microfluidics with low cost, minimized form factors, and improved performance stability. Demonstration of a detachable sweat patch capable of simultaneous recording of cortisol concentration, pH value, and temperature highlights the potential of the "two-part" circuit for advanced, transformative biosensing. The resulting wireless sensors provide a new engineering solution to monitoring biosignals through intimate and seamless integration with skin surfaces.