I'm a physical chemist by training, and I often tell people I "don't believe in zero" - as in, I am very reluctant to say in this case that every material has some electromagnetic frequencies that it simply does NOT absorb at all. BUT, I WILL say that here.
Absorption of energy from an electromagnetic field can happen from several mechanisms. At very low frequencies, electric currents can be induced in metallic materials, giving rise to resistive heating and energy absorption in that way. At low radio frequencies and up into the microwave region, the frequencies of external fields are comparable to the natural rotational motions of groups of molecules, of individual molecules and of parts within them, so energy can be absorbed that way. In the middle and near infrared the motions are bending and stretching of bonds between atoms in molecules. Above that, in the visible, ultraviolet and into the X-ray regions, the energies of the fields are comparable to those of gaps between the energy states of electrons surrounding the atoms. Even higher in frequency and energy are high-energy X-rays and gamma rays that correspond to the energy gaps between states of nuclear particles.
In all these cases, the absorption of energy from an external electromagnetic field happens when the energy of the wave (related to its frequency) matches the difference between two naturally-occurring quantized energy states of an absorber species. In absolutely isolated molecules, atoms, electrons or nuclei, those states are rigidly defined and the energy gap (and hence the frequency of absorbed field) is tightly defined. BUT in the real world all these absorbing species are surrounded by neighbors, each of which creates a small local field that affects the energy state of all nearby bodies. This means the actual energy state of each potential absorber is slightly "perturbed" from its natural state, and hence there is a small to moderate range of energy differences between states, rather than only one isolated energy difference. Thus the absorption does occur over a range of frequencies, sometimes extending into the range of another absorption mechanism nearby. This happens often in the near- and middle-infrared region, and certainly in the visible light region. We see colors in objects because a broad range of overlapping absorptions from multiple electron energy gaps removes some visible colors, leaving others for our eyes to see.So a truly blue object had lost of absorptions in the red-yellow-green regions, and virtually no absorption in the blue and violet regions of visible light. so it definitely has some light frequencies it does NOT absorb.
There is another type of mechanism by which light can be prevented from traveling though an object to reach the other side - reflection and scattering. In these cases the light striking the surface of a body is not absorbed at all, but is reflected off at another direction so it does not penetrate through the body of material. The observer in the "shadow" of the object does not "see" the light (or other electromagnetic wave) not because it was absorbed, but because it was re-directed to another place with no absorption.