Understanding the processes that led Venus to its current state and will drive its future evolution is a major objective of the next generation of orbiters. In this work we analyze the retrieval of the spin vector, the tidal response and the moment of inertia of Venus with VERITAS, a NASA Discovery-class mission. By simulating a systematic joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar we show that VERITAS will provide accuracies (3σ) in the estimates of the tidal Love number k_2 to 4.6×10^(-4), its tidal phase lag to 0.05°, and the moment of inertia factor to 9.8×10^(-4) (0.3% of the expected value). Applying these results to recent models of the Venus interior, we show that VERITAS will provide much improved constraints on the interior structure of the planet.