  We find a topologically non-trivial structure of the Nambu monopole in two
Higgs doublet model (2HDM), which is a magnetic monopole attached by two
topologically stable $Z$ strings ($Z$ flux tubes) from two opposite sides. The
structure is in sharp contrast to the topological triviality of the Nambu
monopole in the standard model (SM), which is attached by a single
non-topological $Z$ string. It is found that the Nambu monopole in 2HDM
possesses the same fiber bundle structure with those of the `t Hooft-Polyakov
monopole and the Wu-Yang description of the Dirac monopole, as a result of the
fact that the electromagnetic gauge field is well-defined even inside the
strings and is non-trivially fibered around the monopole, while the Nambu
monopole in the SM is topologically trivial because electroweak gauge symmetry
is restored at the core of the string. Consequently, the Nambu monopole in 2HDM
can be regarded as an embedding of the 't Hooft-Polyakov monopole into the
$SU(2)_W$ gauge symmetry, and the Dirac's quantization condition always holds,
which is absent for the Nambu monopole in the SM. Furthermore, we construct a
dyon configuration attached with the two strings.
