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The peculiar linear temperature-dependent swelling of core-shell microgels has been conjectured to be linked to the core-shell architecture combining materials of different transition temperatures. Here the structure of pNIPMAM-core and pNNPAM-shell microgels in water is studied as a function of temperature using small-angle neutron scattering with selective deuteration. Photon correlation spectroscopy is used to scrutinize the swelling behaviour of the colloidal particles and reveals linear swelling. Moreover, these experiments are also employed to check the influence of deuteration on swelling. Using a form free multi-shell reverse Monte Carlo approach, the small-angle scattering data are converted into radial monomer density profiles. The comparison of 'core-only' particles consisting of identical cores to fully hydrogenated core-shell microgels, and finally to H core/D shell architectures unambiguously shows that core and shell monomers display gradient profiles with strong interpenetration, leading to cores embedded in shells which are bigger than their isolated 'core only' precursor particles. This surprising result is further generalized to different core cross linker contents, for temperature ranges encompassing both transitions. Our analysis demonstrates that the internal structure of pNIPMAM-core and pNNPAM-shell microgels is heterogeneous and strongly interpenetrated, presumably allowing only progressive core swelling at temperatures intermediate to both transition temperatures, thus promoting linear swelling behaviour.