  In time-reversal symmetry-broken Weyl semimetals, Weyl points act as
monopoles and antimonopoles of the Berry curvature, with a
monopole-antimonopole pair producing a net zero Berry flux. The two-dimensional
(2D) planes that separate a monopole-antimonopole pair of Weyl points carry
quantized Berry flux. In this work, we introduce a class of symmetry-protected
Weyl semimetals which host monopole-antimonopole pairs of Weyl points that
generate a quantized dipolar Berry flux. Consequently, topologically distinct
2D planes coexist in the Brillouin zone, carrying either quantized monopolar or
dipolar flux. We construct a topological invariant -- the staggered Chern
number -- to measure the quantized dipolar flux and employ it to topologically
distinguish between various Weyl points. Finally, through a minimal two-band
model, we investigate physical signatures of bulk topology, including surface
Fermi arcs, zero-energy hinge states, and response to insertion of a $\pi$-flux
vortex.
