In this paper, a new control framework for an insect-scale flapping-wing vehicle is presented that exploits passive aerodynamic effects to stabilize the attitude dynamics. Many flapping-wing robotic flyers and flying insects share a common morphological feature in that the center of mass (CoM) is below the center of pressure (CoP), which makes the hovering configuration intrinsically unstable with open-loop control. Motivated by the fact that the CoM should be ahead of the CoP to ensure the longitudinal stability of the flight dynamics, a new coordinate system is proposed by placing a virtual control point (VCP) above the CoP. The dynamics in the new coordinates are derived using a near-identity diffeomorphism which admits a partial feedback linearization with stable zero dynamics. The behavior of the zero dynamics resembles the dynamics of a 3D pendulum with an aerodynamic damper. An adaptive controller is proposed to make the upright orientation almost globally asymptotically stable over a bounded uncertainty of the aerodynamic drag coefficient. The controller is evaluated in simulation with a Harvard RoboBee following a virtual control point reference trajectory.