Techniques have been developed for discriminating between human and mouse chromosomes, principally to aid the karyotypic analysis of human-mouse hybrids. These methods include fluorescent staining with Hoechst 33258, which causes mouse centromeres to fluoresce more brightly than human centromeres and alkaline staining with Giemsa. Below is the ppt link which may answer your question.
Short Tandem Repeat (STR) analysis is the most powerful tool to authenticate the cell lines. In addition, Molecular Karyotyping (aCGH) and Karyotyping (G-Banded) both useful methods.
More information https://www.creative-bioarray.com/Services/karyotyping-g-banded-service.htm