Phase unwrapping (PU) is an essential procedure in Interferometric Synthetic Aperture Radar (InSAR) and has been studied for decades. The advancement of sensors and platforms has made high-resolution InSAR available, at the same time, and has brought challenges to relative data processing. High-resolution data brings richer details, which could imply massive interference phase discontinuity. Traditional unwrapping methods designed for low- or mediumresolution low-scale data are usually difficult to obtain reliable unwrapping results. How to improve the reliability of wrapped phase data is critical in the design of unwrapping schemes. In this paper, a novel Minimum Balanced Trees (MBT) unwrapping strategy based on comprehensive reliability is presented. The MBT are designed to reconstruct phase discontinuity boundaries with minimum reliability residue pairs, which takes a combined reliability measure of residue distance and phase continuity. Dual residue points of each pair are connected by a line that is expected to be with a weighted minimum L0 norm and is an ideal candidate for the discontinuity boundary. The MBT scheme includes solving eikonal equations, searching for minimum reliability pairs, and spanning detected trees. Most residue points would be covered and organized dynamically. Moreover, for the few uncoupled residues, we employ Flood-Filling on the priority map during path integration. All these procedures can be implemented to run in parallel mode, and the proposed method provides a robust and efficient option for PU, whose advantages are demonstrated in PU experiments on real InSAR wrapped phase data.