We present a new approach for accurate terahertz time-domain spectroscopy of thin films deposited on dielectric substrates. Our approach relies on the simultaneous measurement of film and substrate, allowing for 15 nm-precise determination of the thickness variation between the sample and reference. Our approach allows for unprecedentedly accurate determination of the terahertz conductivity of the thin film. We demonstrate our approach on a 10 nm thin iron film deposited on a 500 μm MgO substrate. We determine the Drude momentum relaxation time in iron to within 0.15 fs uncertainty.