  Within the Halo Model of large scale structure, all matter is contained in
dark matter halos. This simple yet powerful framework has been broadly applied
to multiple data sets and enriched our comprehension of how matter is
distributed in the Universe. In this work we extend this assumption by allowing
for matter to rest not only inside halos but also within cosmic voids and in
between halos and voids (which we call 'dust'). This assumption leads to
additional contributions (1Void, 2Void, Halo-Void, etc.) to the predictions of
correlation functions, spectra and profiles for both halos and voids. Whereas
the Halo Model can only make predictions for halo quantities, the Halo Void
Model extends those for void statistics and halo-void cross-correlations. We
provide recipes for all new ingredients of the Halo Void (Dust) Model, such as
the void abundance, linear bias and density profile and test their validity in
a N-body simulation. Including voids and dust into the calculations improves
the transition between the 1Halo and the 2Halo terms by up to $\sim 6\%$. It
also eliminates the need to include low-mass structures on the normalization of
large-scale terms, suggesting that halos and voids are complementary cosmic
structures to effectively describe matter distribution on large scales of the
Universe.
