Protostars contain icy ingredients necessary for the formation of potential habitable worlds, therefore, it is crucial to understand their chemical and physical environments. This work is focused on the ice features towards the binary protostellar system Ced 110 IRS4A and IRS4B, separated by 250 au and observed with James Webb Space Telescope (JWST) as part of the Early Release Science (ERS) Ice Age collaboration. This study is aimed at exploring the JWST observations of the binary protostellar system Ced 110 IRS4A and IRS4B primarily to unveil and quantify the ice inventories towards these sources. Finally, we compare the ice abundances with those found for the same molecular cloud. We used data from multiple JWST instruments (NIRSpec, NIRCam, and MIRI) to identify and quantify ice species in the Ced 110 IRS4 system. The analysis was performed by fitting or comparing the laboratory infrared spectra of ices to the observations. Spectral fits are carried out with the ENIIGMA fitting tool that searches for the best fit out of a large number of solutions. The degeneracies of the fits are also addressed and the ice column densities are calculated. In cases where the full nature of the absorption features is not yet known, we explore different laboratory ice spectra to compare them with the observations. We provide a list of securely and tentatively detected ice species towards the primary and the companion sources. For Ced 110 IRS4B, we detected the major ice species H_2O, CO, CO_2, and NH_3. All species are found in a mixture except for CO and CO_2, which have both mixed and pure ice components. In the case of Ced 110 IRS4A, we detected the same major species as in Ced 110 IRS4B, as well as the following minor species: CH_4, SO_2, CH_3OH, OCN^-, NH_4^+, and HCOOH. A tentative detection of N_2O ice (7.75 μm), forsterite dust (11.2 μm), and CH_3^+ gas emission (7.18 μm) in the primary source was also made. Compared with the two lines of sight towards background stars in the Chameleon I molecular cloud, the protostar exhibits similar ice abundances, except in the case of the ions that are higher in IRS4A. The most clear differences are the absence of the 7.2 and 7.4 μm absorption features due to HCOO^- and icy complex organic molecules in IRS4A. There is also evidence of thermal processing in both IRS4A and IRS4B, as probed by the CO_2 ice features. We conclude that the binary protostellar system Ced 110 IRS4A and IRS4B has a large inventory of icy species. The similar ice abundances in comparison to the starless regions in the same molecular cloud suggests that the chemical conditions of the protostar were set at earlier stages in the molecular cloud. It is also possible that the source inclination and complex geometry cause a low column density along the line of sight, which hides the bands at 7.2 and 7.4 μm. Finally, we highlight that a comprehensive analysis using radiative transfer modelling is needed to disentangle the spectral energy distributions of these sources.