Biosensors based on organic field-effect transistors can offer mechanical flexibility, stretchability and operational stability for conformal on-skin monitoring. However, bending, stretching, moisture and temperature changes can lead to signal artefacts and drifts. Here we report skin-like drift-free biosensors based on stretchable diode-connected organic field-effect transistors. Our approach relies on capacitive coupling and the subtraction of interference signals using two extended gates functionalized separately with target and reference bioreceptors. It reduces signal distortion by up to two orders of magnitude compared with an unconnected organic field-effect transistor, despite changes in the sampling environment, including bias stress instability, uniaxial strain (up to 100%), compression (up to 50 mN) and temperature variations (25–40 °C). We apply the approach to aptamer-based sensing for cortisol, enzyme-based sensing for glucose and ion-selective membrane-based potentiometric sensing for sodium ions. We also develop a hybrid wearable system, including soft sensors and a flexible printed circuit board, which wirelessly communicates with a smartphone app. We show that the system can perform cortisol sensing from human sweat under acute stress events.