Space radiation hazards are recognized as a key concern for human space flight. For long-term interplanetary missions, they constitute a potentially limiting factor since current protection limits for low-Earth orbit missions may be approached or even exceeded. In such a situation, an accurate risk assessment requires knowledge of equivalent doses in critical radiosensitive organs rather than only skin doses or ambient doses from area monitoring. To achieve this, the MATROSHKA experiment uses a human phantom torso equipped with dedicated detector systems. We measured for the first time the doses from the diverse components of ionizing space radiation at the surface and at different locations inside the phantom positioned outside the International Space Station, thereby simulating an extravehicular activity of an astronaut. The relationships between the skin and organ absorbed doses obtained in such an exposure show a steep gradient between the doses in the uppermost layer of the skin and the deep organs with a ratio close to 20. This decrease due to the body self-shielding and a concomitant increase of the radiation quality factor by 1.7 highlight the complexities of an adequate dosimetry of space radiation. The depth-dose distributions established by MATROSHKA serve as benchmarks for space radiation models and radiation transport calculations that are needed for mission planning.