Aims. We investigate the morphology at low radio frequencies of the supernova remnant (SNR) IC 443 in detail and accurately establish its radio continuum spectral properties. Methods. We used the VLA in multiple configurations to produce high-resolution radio images of IC 443 at 74 and 330 MHz. From these data we produced the first sensitive, spatially resolved spectral analysis of the radio emission at long wavelengths. The changes with position in the radio spectral index were correlated with data in near infrared (NIR) from 2MASS, in gamma-rays from VERITAS, and with the molecular 12 CO (J = 1−0) line emission. With the available statistics the VERITAS γ-ray emission strikingly matches the CO distribution, but no clear evidence is found for a morphological correlation between the TeV distribution and radio emission. Conclusions. The excellent correspondence between the eastern radio flattest spectrum region and NIR ionic lines strongly suggests that the passage of a fast, dissociating J-type shock across the interacting molecular cloud dissociated the molecules and ionized the gas. We therefore conclude that thermal absorption at 74 MHz (τ 74 up to ∼0.3) is responsible for the localized spectral index flattening observed along the eastern border of IC 443. Towards the interior of IC 443, the spectrum is consistent with those expected from linear diffusive shock acceleration, while the flatter spectrum in the southern ridge is a consequence of the strong shock/molecular cloud interaction.