  We introduce a generalized non-uniform mean-field formalism to describe the
dissociation of weak rod-like polyelectrolytes (PEs). Our approach allows for
two-sublattice symmetry breaking which in titration curves is associated with a
plateau for intermediate dissociation degrees. We first test our method in the
case of a single weak PE by comparison with exact enumeration studies and show
that it gives quantitatively accurate results for the dissociation degree in
the full range of pH values, and in specific performs much better than the
nearest-neighbor approximation (where exact solutions are possible). We then
study charge regulation of the coupled system of a weak polyacid and a weak
polybase as a function of their mutual distance, which has some relevance for
PE-multilayer formation and for PE complexation. An intricate interplay of the
degree of dissociation and the effective interaction between the PEs as a
function of their mutual distance is found.
