Accurate phase demodulation is critical for vital sign detection using millimeter-wave radar. However, in complex environments, time-varying DC offsets and phase imbalances can severely degrade demodulation performance. To address this, we propose a novel DC offset calibration method alongside a Hilbert and Differential Cross-Multiply (HADCM) demodulation algorithm. The approach estimates time-varying DC offsets from neighboring signal peaks and valleys, then employs both differential forms and Hilbert transforms of the I/Q channel signals to extract vital sign information. Simulation and experimental results demonstrate that the proposed method maintains robust performance under low signal-to-noise ratios. Compared to existing demodulation techniques, it offers more accurate signal recovery in challenging scenarios and effectively suppresses noise interference.