Reflected light micro-interferometry was used to observe stratification (i.e., the kinetics of layered structuring) in thinning foam films formed from micellar solutions of sodium n-alkyl sulfates at concentrations much lower than those at which liquid crystalline structures form in bulk solutions. The effects of surfactant concentration and chain length, added electrolyte, and capillary pressure on the step-wise jump transition thicknesses have been investigated. We have further conducted a model study with films formed from aqueous dispersions of latex particles. In similar fashion to those formed from micellar solutions, the thinning films changed thickness with regular step-wise jump transitions, and the films exhibited a number of metastable equilibria. These observations verify that the stratification of thin liquid films can be explained as a layer-by-layer thinning of ordered structures of micelles or colloidal particles formed inside the film. The stratification-nonstratification phase diagram is presented for anionic micelles and is similar to the order-disorder phase diagram for latexes. In the accompanying paper (Part II) we show that the phenomenon of stratification and ordered micellar structures is governed by the long range electrostatic repulsion beteen the ionic micelles and the restricted volume of the film. This present study provides evidence, for the first time, for the presence of structural forces in thin films with thicknesses on the order of 100 nm and strongly suggests that the free liquid film dynamics may be used as a probe to study the ordering in, and stability of, microheterogeneous systems.