We construct two-fluid equilibrium configurations for neutron stars (NSs) with magnetic fields, using a self-consistent and non-linear numerical approach. The two-fluid approach – likely to be valid for large regions of all but the youngest NSs – provides us with a straightforward way to introduce stratification and allows for more realistic models than the ubiquitous barotropic assumption. In all our models, the neutrons are modelled as a superfluid, whilst for the protons we consider two cases: one where they are a normal fluid and another where they form a type II superconductor. We consider a variety of field configurations in the normal-proton case and purely toroidal fields in the superconducting case. We find that stratification allows for a stronger toroidal component in mixed-field configurations, though the poloidal component remains the largest in all our models. We provide quantitative results for magnetic ellipticities of NSs, both in the normal- and superconducting-proton cases.