This was done with the moon: Radio Dishes Peer Beneath Moon's Surface
It is important to understand how this process works. The method described in your article is known as Bistatic Radar. In effect, a transmitter sends out a signal (generally a radio telescope in the microwave region) which hits the surface of some body and bounces off to be received back on Earth by a second, separate radio telescope. Now, because a microwave's wavelength is so long ($\sim 0.1-100\:cm$) the microwaves don't bounce off from the exact surface, but instead are able to penetrate slightly into the subsurface before being reflected. This means the receiver gets a reflection of the subsurface of the body.
In the case you linked, they used the Arecibo Telescope to provide the transmitted signal to the Moon and the Green Bank Telescope to receive the signal. A similar process could be done to other bodies besides our Moon. However, you run into the problem that the farther away an object is, the harder it will be to detect the returning signal.
I believe that most objects within our solar system (and certainly all objects outside it) are outside the distance where this method will work. I was able to find an instance where someone used this method for an asteroid that passed by the Earth at a distance 11 times that of the Moon. I'm not sure what the limit is to how far away something must be before this method no longer works, but I imagine it wouldn't work even for Mars unless we seriously upgrade our technology and power.
Of course your question seems to presuppose the transmitter and receiver are both on Earth. If your transmitter is much closer, say a satellite orbiting that planet, then it is certainly feasible. Here is a source which discusses the concept of using Bistatic Radar probing via a satellite, which also goes into the history a bit on what has been done before.