We show that energetic considerations enforce a Hopf fibration of the standard model topology within the 2HDM whose potential has either an SO(3) or U(1) Higgs-family symmetry. This can lead to monopole and vortex solutions. We find these solutions, characterize their basic properties and demonstrate the nature of the fibration along with the connection to Nambu's monopole solution. We point out that breaking of the U(1)_{EM} in the core of the defect can be a feature which leads to a nonzero photon mass there.