We present observations of the symbiotic star CH Cyg with a new JHK-band beam combiner mounted to the IOTA interferometer. The new beam combiner consists of an anamorphic cylindrical lens system and a grism, and allows the simultaneous recording of spectrally dispersed J-, H- and K-band Michelson interferograms. The observations of CH Cyg were conducted on 5, 6, 8 and 11 June 2001 using baselines of 17m to 25m. From the interferograms of CH Cyg, J-, H-, and K-band visibility functions can be determined. Uniform-disk fits to the visibilities give, e.g., stellar diameters of (7.8 ± 0.6) mas and (8.7 ± 0.8) mas in H and K, respectively. Angular stellar filter radii and Rosseland radii are derived from the measured visibilities by fitting theoretical center-to-limb intensity variations (CLVs) of Mira star models. The available HIPPARCOS parallax of CH Cyg allows us to determine linear radii. For example, on the basis of the K-band visibility, Rosseland radii in the range of 214 to 243 solar radii can be derived utilizing CLVs of different fundamental mode Mira models as fit functions. These radii agree well within the error bars with the corresponding theoretical model Rosseland radii of 230 to 282 solar radii. Models of first overtone pulsators are not in good agreement with the observations. The wavelength dependence of the stellar diameter can be well studied by using visibility ratios V(λ1)/V(λ2) since ratios of visibilities of different spectral channels can be measured with higher precision than absolute visibilities. We found that the 2.03 μm uniform disk diameter of CH Cyg is approximately 1.1 times larger than the 2.15 μm and 2.26 μm uniform-disk diameter.