We introduce a certain construction which allows us to characterize bi-Lagrangian manifolds with a flat canonical connection without referring to the connection itself. It turns out that one can probe the curvature of such manifolds using a geometric invariant of its 2-dimensional symplectic submanifolds called "reflection holonomy", inspired by the works of W. Blaschke, G. Bol and G. Thomsen on planar 3-webs. The aim of the talk is to define this invariant and to show how its triviality leads to the local triviality of the bi-Lagrangian structure under consideration.