Microstructured optical products are becoming more widespread due to advances in manufacturing. Many of these structures contain faceted surfaces with steep slopes. Adequate metrology for such surfaces is lacking. We describe an interferometric technique that combines plane wave illumination with an index matching liquid to achieve high quality, high speed measurements of such faceted microstructures. We account for refraction at the interfaces, rather than consider only optical path length changes due to the index liquid, and this significantly improves the facet angle measurement. We demonstrate the technique with the measurement of an array of micropyramids and show that our results are in good agreement with measurements taken on a contact profilometer. We also extend the technique to measure opaque microcorner cubes by implementing an intermediate replication step.