  Because of their period-luminosity relation (PLR), classical Cepheids play a
key role in the calibration of the extragalactic distance scale and the
determination of the Hubble-Lema\^{i}tre constant $H_0$. Recent findings show
that the majority of classical Cepheids should be in binary or multiple
systems, which might undermine their accuracy, as the extra -- and unaccounted
for -- light from the companions of Cepheids causes a shift in the PLR. We
quantify this shift using synthetic populations of binary Cepheids that we
developed for this purpose, as described in Paper I of this series. We find
that while all PLRs are shifted toward brighter values due to the excess light
from the companions, the bias in the relative distance modulus between two
galaxies hosting binary Cepheids can be either positive or negative, depending
on the percentage of binary Cepheids in them. If the binarity percentage in the
two galaxies is similar, the effect of binarity is canceled. Otherwise, it
introduces a shift in the distance modulus of the order of millimags in the
near-infrared passbands and Wesenheit indices, and tens of millimags in the
visual domain; its exact value depends on the variant of the synthetic
population (a unique combination of metallicity, star formation history, shape
and location of the instability strip, and initial parameter distributions).
Such shifts in distance moduli to type Ia supernova host galaxies introduce an
additional statistical error on $H_0$, which however does not prevent measuring
$H_0$ with a precision of 1%.
