We investigate simultaneous state-insensitive trapping of a mixture of two different atomic species, Caesium and Rubidium. The magic wavelengths of the Caesium and Rubidium atoms are different, $935.6$ nm and $789.9$ nm respectively, thus single-frequency simultaneous state-insensitive trapping is not possible. We thus identify bichromatic trapping as a viable approach to tune the two magic wavelengths to a common value. Correspondingly, we present several common magic wavelength combinations appropriate for simultaneous state-insensitive trapping of the two atomic species.