The formation and quadratic nonlinearity of a multiple hydrogen-bonded 1:1 supramolecular complex 1.2 between the 2,6-diaminopyridine-based Lambda-shaped molecule, 1, and ferrocenyl barbituric acid, 2, in solution have been investigated by the hyper-Rayleigh scattering (HRS) and NMR techniques. A 6-fold increase in the molecular hyperpolarizability (beta) of the complex 1.2 over the sum of the molecular hyperpolarizabilities of the components 1 and 2 is seen. Such a significant enhancement in beta is attributed to the alignment of the molecular dipoles of 1 and 2 in the 2D plane leading to the creation of a large dipole moment in the plane of the supramolecular complex. Depolarized HRS experiments led to the determination of the in-plane polarization components of beta of the supramolecular complex 1.2. The component of beta in the direction of the dipole moment is large. This investigation exemplifies the role of multiple hydrogen bonds in stabilizing a 2D supramolecular architecture leading to a large enhancement of molecular nonlinearity.