Bubble detectors have been used to characterise the neutron dose and energy spectrum in several modules of the International Space Station (ISS) as part of an ongoing radiation survey. A series of experiments was performed during the ISS-34, ISS-35, ISS-36 and ISS-37 missions between December 2012 and October 2013. The Radi-N2 experiment, a repeat of the 2009 Radi-N investigation, included measurements in four modules of the US orbital segment: Columbus, the Japanese experiment module, the US laboratory and Node 2. The Radi-N2 dose and spectral measurements are not significantly different from the Radi-N results collected in the same ISS locations, despite the large difference in solar activity between 2009 and 2013. Parallel experiments using a second set of detectors in the Russian segment of the ISS included the first characterisation of the neutron spectrum inside the tissue-equivalent Matroshka-R phantom. These data suggest that the dose inside the phantom is ∼70 % of the dose at its surface, while the spectrum inside the phantom contains a larger fraction of high-energy neutrons than the spectrum outside the phantom. The phantom results are supported by Monte Carlo simulations that provide good agreement with the empirical data.