Emergence of products that feature functional surfaces with complex geometries, such as freeform optics in consumer electronics and augmented reality and virtual reality, requires high-accuracy non-contact surface measurement. However, large discrepancies are often observed between the measurement results of optical methods and contact stylus methods, especially for complex surfaces. For interference microscopy, such as coherence scanning interferometry, the three-dimensional surface transfer function provides information about the instrument spatial frequency passband and about lens aberrations that can result in measurement errors. Characterisation and phase inversion of the instrument's three-dimensional surface transfer function yields an inverse filter that can be applied directly to the three-dimensional fringe data. The inverse filtering is shown to reduce measurement errors without using any data processing or requiring any a priori knowledge of the surface. We present an experimental verification of the characterisation and correction process for measurements of several freeform surfaces and an additive manufactured surface. Corrected coherence scanning interferometry measurements agree with traceable contact stylus measurements to the order of 10 nm.