Density-density correlations in a planar interface of a neutral, multi-component fluid mixture are analysed. For a ‘normal’ liquid-gas or liquid-liquid interface the transverse (parallel to the interface) correlations exhibit Ornstein-Zernike behaviour with a common correlation length ξT = (σ/b)1/2, where σ is the surface tension and b is determined by the external fields. If, however, the interface corresponds to a near complete wetting situation so that a thick film of a third fluid phase (β) intrudes between the two bulk phases α and γ, the transverse correlations do not, in general, exhibit Ornstein-Zernike behaviour. Rather they exhibit more complex structure for small transverse wave numbers which depends on the ‘stiffness’ of the wetting film. In the limit of a very thick film Ornstein-Zernike behaviour occurs in both edges, the correlation length depending on the value of σ and b appropriate to the individual interface so that ξαβ T = (σαβ/b αβ)1/2 and ξβγ T = (σβγ/b βγ)1/2. The theoretical analys...