Two sets of core-shell microgels composed of temperature-sensitive poly(N-isopropylacrylamide) (PNiPAM) with different spatial distribution of pH-sensitive methacrylic acid (MAA) groups were prepared. The cores consist of either PNiPAM (neutral core; nc) or PNiPAM-co-MAA (charged core; cc). A charged shell existing of PNiPAM-co-MAA was added to the neutral core (yielding neutral core-charged shell; nccs), on the charged core, on the other hand, a neutral shell of PNiPAM was added (charged core-neutral shell; ccns). Complexes of these microgels with positively charged poly(diallyldimethylammonium chloride) (PDADMAC) of different molar masses were prepared. The amount of bound polyelectrolyte was quantified, and the microgel-polyelectrolyte complexes were characterized with respect to electrophoretic mobility and hydrodynamic radius. The penetration of polyelectrolyte into the microgel was also monitored by means of lifetime analysis of a fluorescent dye covalently bound to poly(L-lysine) providing information on the probe's local environment. The architecture of the microgel has a significant influence on the interaction with oppositely charged polyelectrolyte. Complexes with microgel with the charged shell tend to flocculate at charge ratios of 1 and are thus similar to polyelectrolyte complexes with rigid colloidal particles. Complexes with microgels that consist of a charged core and a neutral shell show very different properties: They are still temperature sensitive and reveal an influence of the polyelectrolyte's chain length. Low molecular weight PDADMAC can penetrate through the neutral shell into the charged core, and thus nearly no charge reversal occurs. The high-MW polyelectrolyte does not penetrate fully and leads to charge reversal. The results demonstrate that microgels are able to absorb or adsorb polyelectrolytes depending on the polyelectrolyte's chain length and the microgels architecture. Complexes with different surface properties and different colloidal stability can be prepared, and polyelectrolytes can be encapsulated in the microgel core. Thus, multisensitive core-shell microgels combine permeability and compartmentalization on a nanometer length scale and provide unique opportunities for applications in controlled uptake and release.