Co‐Al2O3 composite films were produced by electron‐beam coevaporation in a system with elaborate process control. The deposits were analyzed by transmission electron microscopy, electron diffraction, Auger electron spectroscopy, secondary ion mass spectroscopy, Rutherford backscattering, field ion microscopy, mechanical stylus measurements, and electrical dc and ac measurements. A uniform separated‐grain structure with regular hcp Co particles embedded in Al2O3 was found for Co contents (fCos’) up to ∼30 vol %. The complex dielectric permeability ϵ¯ was evaluated in the 0.3≲λ≲40‐μm wavelength range for samples with 0.11≲ fCo ≲0.60 by carefully selected combinations of spectrophotometric transmittance and reflectance data. Numerical accuracy and internal consistency were investigated. Effective medium theories for ϵ¯ were derived by applying classical scattering theory to spherical random unit cells defined so as to properly represent a number of typical microgeometries. The formulations due to Maxwell Garnett, Bruggeman, and others were thus rederived in a unified way. Large‐size limits of validity and extensions to nonspherical particles were treated. It was found that the Maxwell Garnett theory could reproduce the experimental ϵ¯’s in detail at low fCo provided that some Co was taken to be dispersed in the insulating matrix. At larger fCo’s we found discrepancies which are likely to be due mainly to dipole‐dipole coupling among adjacent particles. A comparison of the experimental ϵ¯’s and the rigorous Bergman–Milton bounds, which hold irrespective of detailed microgeometry, gave several interesting results: the ϵ¯’s varied monotonically along one of t- he bounds for isotropic materials as fCo was increased, at large fCo we found evidence for anisotropy, and at λ≊12.5 μm we noted certain cases of disagreement with even the most generous bounds. The empirical ϵ¯’s were used to construct surfaces which combine a high solar absorptance as with a low hemispherical thermal emittance eH. From a computer optimization study we found that as =0.95 and eH =0.07 could be obtained with 0.07 μm of Co‐Al2O3 ( fCo≊0.6) antireflected with 0.07 μm of Al2O3 and laid on Ni. These results were verified by measurements on samples which approximate the ideal design.