Multiplex fluorescence in situ hybridization (M-FISH) is a recently developed technology that enables multi-color chromosome karyotyping for molecular cytogenetic analysis. Each M-FISH image set consists of a number of aligned images of the same chromosome specimen captured at different optical wavelength. This paper presents embedded M-FISH image coding (EMIC), where the foreground objects/chromosomes and the background objects/images are coded separately. We first apply critically sampled integer wavelet transforms to both the foreground and the background. We then use object-based bit-plane coding to compress each object and generate separate embedded bitstreams that allow continuous lossy-to-lossless compression of the foreground and the background. For efficient arithmetic coding of bit planes, we propose a method of designing an optimal context model that specifically exploits the statistical characteristics of M-FISH images in the wavelet domain. Our experiments show that EMIC achieves nearly twice as much compression as Lempel-Ziv-Welch coding. EMIC also performs much better than JPEG-LS and JPEG-2000 for lossless coding. The lossy performance of EMIC is significantly better than that of coding each M-FISH image with JPEG-2000.