Measuring microcombs in amplitude and phase provides unique insight into the nonlinear cavity dynamics, but spectral phase measurements are experimentally challenging. Here, we report a linear heterodyne technique assisted by electro-optic downconversion that enables differential phase measurement of such spectra with unprecedented sensitivity (-50 dBm) and bandwidth coverage (>110 nm in the telecommunications range). We validate the technique with a series of measurements, including single-cavity and photonic molecule microcombs.