Quantum technology based on cold-atom interferometers is showing great promise for fields such as inertial sensing and fundamental physics. However, the finite free-fall time of the atoms limits the precision achievable on Earth, while in space interrogation times of many seconds will lead to unprecedented sensitivity. Here we realize simultaneous 87 Rb– 39 K interferometers capable of operating in the weightless environment produced during parabolic flight. Large vibration levels (10 À 2 g Hz À 1/2), variations in acceleration (0–1.8 g) and rotation rates (5° s À 1) onboard the aircraft present significant challenges. We demonstrate the capability of our correlated quantum system by measuring the Eötvös parameter with systematic-limited uncertainties of 1.1 Â 10 À 3 and 3.0 Â 10 À 4 during standard-and microgravity, respectively. This constitutes a fundamental test of the equivalence principle using quantum sensors in a free-falling vehicle. Our results are applicable to inertial navigation, and can be extended to the trajectory of a satellite for future space missions.