  We study the multi-charged moments for two disjoint intervals in the ground
state of two $1+1$ dimensional CFTs with central charge $c=1$ and global $U(1)$
symmetry: the massless Dirac field theory and the compact boson (Luttinger
liquid). For this purpose, we compute the partition function on the higher
genus Riemann surface arising from the replica method in the presence of
background magnetic fluxes between the sheets of the surface. We consider the
general situation in which the fluxes generate different twisted boundary
conditions at each branch point. The obtained multi-charged moments allow us to
derive the symmetry resolution of the R\'enyi entanglement entropies and the
mutual information for non complementary bipartitions. We check our findings
against exact numerical results for the tight-binding model, which is a lattice
realisation of the massless Dirac theory.
