It was shown by Ozawa that the amalgamated free product of two exact groups over an amenable group is biexact relative to the two generating groups. In this talk, I will show that the amalgamated free product of weakly exact von Neumann algebras over an injective von Neumann subalgebra is relatively biexact, generalizing the case of groups. The proof involves a universal property of Toeplitz-Pimsner algebras and a locally convex topology on bimodules of von Neumann algebras, which is used to characterize biexactness for von Neumann algebras.