How does ice-penetrating radar "see" through kilometers of ice without being absorbed?
Water molecules do interact with microwaves and in microwave ovens that operate at 900MHZ- 2.5GHz. This Radar instrument operates using Very High Freq Radio Waves at 193MHz [1].

At lower-than-microwave frequencies, the loss factor is much lower, and as a result the wave can penetrate deeper into the ice sheet with minimal absorption. The difference in permittivities between liquid water and solid ice is what allows them to visualise boundaries and identify the subglacial lakes

From Nasa [2]


  Ice, on the other hand reacts differently depending on the radar's frequency. It reflects high-frequency radio waves, but despite being solid, lower frequency radar can pass through ice to some degree. This is why MCoRDS uses a relatively low frequency—between 120 and 240 MHz. This allows the instrument to detect the ice surface, internal layers of the ice and the bedrock below. "To sound the bottom of ice you have to use a lower frequency," said John Paden, CReSIS scientist. "Too high a frequency and signal will be lost in the ice."