The shocked interstellar medium around IC 443 produces strong X-ray emission in the soft energy band (E 1.5 keV). We present an analysis of such emission as observed with the EPIC MOS cameras on board the XMM-Newton observatory, with the purpose to find clear signatures of the interactions with the interstellar medium (ISM) in the X-ray band, which may complement results obtained in other wavelengths. We found that the giant molecular cloud mapped in CO emission is located in the foreground and gives an evident signature in the absorption of X-rays. This cloud may have a torus shape, and the part of torus interacting with the IC 443 shock gives rise to 2MASS Ks emission in the southeast. The measured density of emitting X-ray-shocked plasma increases toward the northeastern limb, where the remnant is interacting with an atomic cloud. We found an excellent correlation between emission in the 0.3-0.5 keV band and bright optical/radio filament on large spatial scales. The partial shell structure seen in this band therefore traces the encounter with the atomic cloud.