High-harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in the amplitude and phase of high-harmonic generation (HHG) signals. However, measurement of the harmonic phase is a daunting task. Here, we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to ~3 attoseconds ($1\text{as}={10}^{-18}\text{s}$) time delay which is nearly independent of harmonic order. The measurements agree very well with numerical calculations of a four-dimensional time-dependent Schödinger equation. Numerical simulations also reveal the effects of molecular orientation and intramolecular two-center interference on the measured phase difference. This technique opens a new avenue for measuring the phase of harmonic emission for different atoms and molecules. Together with isomeric or isotopic comparisons, it also enables the observation of subtle effects of molecular structures and nuclear motion on electron dynamics in strong laser fields.