Based on the property analysis of interferential multispectral images, a novel compression algorithm of partial set partitioning in hierarchical trees (SPIHT) with classified weighted rate-distortion optimization is presented. After wavelet decomposition, partial SPIHT is applied to each zero tree independently by adaptively selecting one of three coding modes according to the probability of the significant coefficients in each bitplane. Meanwhile the interferential multispectral image is partitioned into two kinds of regions in terms of luminous intensity, and the rate-distortion slopes of zero trees are then lifted with classified weights according to their distortion contribution to the constructed spectrum. Finally a global rate-distortion optimization truncation is performed. Compared with the conventional methods, the proposed algorithm not only improves the performance in spatial domain but also reduces the distortion in spectral domain.