Two modifications of the interdigital accelerating H structure forming the basis for upgrading both the main and prestripper sections of the Kharkov multicharged ion linac (MILAC) are described. Possible application of this type of structure to heavy ion accelerator is discussed. It is shown that the use of the interdigital H structure in this particular case has enabled three major problems to be solved, namely: (i) to increase the operating wavelength from 2.1 m of the previously used Alvarez structure up to 6.3 m, (ii) to double the acceleration rate, and (iii) to increase the shunt impedance by 2–4 times. New methods and designs are described for tuning the cavities at an operating frequency and transforming the sinusoidal field distribution, peculiar to the H mode, into the homogeneously distributed field along the structure axis, with varying period lengths. Characteristics of the MILAC main and prestripper sections are given.