Assuming an oriented molecular layer to behave optically as a homogeneous, uniaxial medium with its optic axis normal to the interface, such a system is treated theoretically to yield equations relevant to both specular reflectance and ellipsometric spectroscopy. Explicit expressions are derived for the empirical quantities (relating them to the optical constants of the media and other system parameters) which are both reasonably simple and correct to second-order terms in the film thickness. From ellipsometric measurements alone, it is not possible to distinguish between very thin uniaxial and isotropic films. However, data for a very thin non-absorbing uniaxial film on an absorbing substrate (e.g., a metal), if analyzed on the assumption of film isotropy, lead to an apparent absorption index for the film of the magnitude of the absorption index found for semi-conductors. A similar result is predicted for specular reflectance measurements, except that in that case the apparent optical constants of the film depend on the angle of incidence.