Short answer: Yes, the gravitational field goes through everything.

Longer answer. There are three ways to model the gravitational field, depending on the frame of reference, whether macroscopic, microscopic, or very large gravitational masses.

Macroscopic is the classical [Newtonian gravitational model][1] where there exists a gravitational field due to masses.

Large gravitational masses are modeled with [General Relativity][2] , and there space time itself describes the behavior of large masses, and the classical field emerges from the space distortions

The microscopic needs quantization, and that is where one expects to find gravitons, the corresponding exchange particle to photons for electromagnetic interactions.  The gravitational force is the [weakest force][3] among the four, and gravitons, if they exist, can go through everything  interacting extremely weakly , in addition to being the carrier of the gravitational force.

The classical field as well as the General Relativity formalism are expected in a future theory to smoothly emerge from the quantized version of gravity, but this is still at the research stage.


  [1]: https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
  [2]: https://en.wikipedia.org/wiki/General_relativity
  [3]: http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html