The core of a neutron star is 100% neutrons (or perhaps a quark-gluon plasma where no individual neutrons are distinguishable). All the electrons and protons have been crushed together (by the extreme gravity) until they merge and form neutrons. As you get further away from the core, you find more and more protons and electrons, but still no atoms. The surface layer of the star has distinct atomic nuclei, but since the surface temperature is so hot (600,000K) they are not neutral atoms; the electrons are not bound to the nuclei. The density at the surface is still about a thousand times higher than the density of water or stone.