Multibaseline (MB) phase unwrapping (PU) is a key processing technique in MB interferometric synthetic aperture radar (InSAR). As one of the most popular methods, the cluster analysis (CA)-based MBPU method often suffers from the problem of low noise robustness. Therefore, the block-matching and 3D filtering (BM3D) algorithm, one of the most effective filtering methods for image denoising, is applied to improve the performance of the method. Five different filtering strategies for applying BM3D are proposed in the paper: interferogram filtering (IFF), intercept filtering (ICF), cluster number filtering (CNF), unwrapped phase filtering (UPF), and simultaneous filtering (STF). In particular, while keeping the general structure of BM3D, four different similarity measures are defined for interferograms, intercepts, clusters, and unwrapped phases to accommodate the special characteristics of different filtering objects. Experiments on synthesized and real InSAR datasets prove their feasibility and effectiveness, and the experiment results show that (1) the PU accuracy and robustness of the CA-based MBPU method can be greatly improved by adding BM3D denoising; (2) simultaneous filtering of interferograms, intercepts, cluster numbers, and unwrapped phases works best, but with the worst time complexity; (3) when filtering is performed for only one object of the CA-based MBPU method, the filtering effect of CNF and UPF is better than that of IFF and ICF; and (4), considering the three indicators of PUSR, NRSE, and time consumption, CNF and UPF should be the best choices.