This paper presents the absorbed dose and dose equivalent rate measurements achieved with the DOSimetry TElescope (DOSTEL) during the two Matroshka (MTR) experiment campaigns in 2004/2005 (MTR-1) and 2007/2008 (MTR-2B). The comparison between the inside (MTR-2B) and outside (MTR-1) mission has shown that the shielding thickness provided by the International Space Station (ISS) spacecraft hull has a minor effect on the radiation exposure caused by Galactic Cosmic Rays (GCR). The exposure varies with the solar modulation of the GCR, too. Particles from Earth’s radiation belts are effectively shielded by the spacecraft hull, and thus the contribution to the radiation exposure is lower for the inside measurement during MTR-2B. While the MTR-DOSTEL absorbed dose rate shows a good agreement with passive detectors of the MTR experiment for the MTR-2B mission phase, the MTR-1 absorbed dose rates from MTR-DOSTEL measurements are much lower than those obtained by a nearby passive detector. Observed discrepancies between the MTR-DOSTEL measurements and the passive detectors located nearby could be explained by the additional exposure to an enhanced flux of electrons trapped between L-parameter 2.5 and 3.5 caused by solar storms in July 2004.