To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We observe that an asymmetric obstacle (cambered airfoil profile) experiences a downwards lift, opposite to the lift usually known (in a different context) in aerodynamics. Correlations of velocity, deformations, and pressure fields yield a clear explanation of this inverse lift, involving the elasticity of the foam. We argue that such an inverse lift is likely common to complex fluids with elasticity.