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We present a comprehensive analysis of the applicability of the effective medium approximation to deeply subwavelength (period all-dielectric multilayer structures. We demonstrate that even though the dispersion relations for such multilayers differ from the effective medium prediction only slightly, there can be regimes when an actual multilayer stack exhibits significantly different properties compared to its homogenized model. In particular, reflection near the critical angle is shown to strongly depend on even very small period variations, as well as on the choice of the multilayer termination. We identify the geometries for which the influence of the subwavelength features is maximized and demonstrate that the difference between the reflectance from the actual multilayer and the effective medium prediction can be as great as 0.98. The results of this analysis can be useful for high-precision multilayer ellipsometry and in sensing applications. [ABSTRACT FROM AUTHOR]