We report an experimental method that combines nonlinear-crystal-based transient detection imaging (TDI) with interferometric complex-field retrieval. The system allows measuring both phase and amplitude of a dynamic scene while suppressing stationary background. Theoretical and experimental results prove the linear relation existing between input and output phases, as well as the benefits of phase analysis for both detection and measurement with high resolutions of λ/30, even under noisy conditions. Additionally, we present experimental evidence of the remarkable ability of the technique to detect phase sign changes in the scene -what we call differential-phase TDI- showing great detection sensitivity and no calibration requirements.