The molecular organization in monolayers of deuterated cadmium arachidate deposited on solid metallic and dielectric substrates or spread at the air/water interface is investigated using different techniques of Fourier transform infrared spectroscopy, For metals, the polarization modulated reflectivity shows that the molecules have a high molecular order and are oriented quasi perpendicularly with respect to the surface. The in-plane organization is determined by complementary transmission experiments on CaF2 plates. The CD2 bending vibration in mono- and multilayer Langmuir-Blodgett stacks reveals the hexagonal packing of a single monolayer irrespective of the hydrophilic or hydrophobic character of the substrate. Probing the stack organization using selective monolayer deuteration in hydrogenated Langmuir-Blodgett films shows that the first deposited monolayer of an odd-numbered stack keeps its hexagonal structure while additional bilayers adopt an orthorhombic packing induced by the strong polar head/head interactions, However a monolayer may have an orthorhombic arrangement either if it is deposited on an orthorhombic commensurable substrate or if it is at a low temperature in which case intermolecular interactions are strengthened. Finally, differential reflectivity allows a single monolayer spread at the air/water interface to be studied. It is shown that such a Langmuir film is arranged in a two-dimensional hexagonal packing with its alkyl chains oriented perpendicularly with respect to the surface and its COO- polar groups symmetrically anchored at the interface.