  In original twin Higgs model, vacuum misalignment between electroweak and new
physics scales is realized by adding explicit $\mathbb{Z}_2$ breaking term.
Introducing additional twin Higgs could accommodate spontaneous $\mathbb{Z}_2$
breaking, which explains the origin of this misalignment. We introduce a class
of two twin Higgs doublet models with most general scalar potential, and
discuss general conditions which trigger electroweak and $\mathbb{Z}_2$
symmetry breaking. Various scenarios on realising the vacuum misalignment are
systematically discussed in a natural two Higgs double model framework:
explicit $\mathbb{Z}_2$ breaking, radiative $\mathbb{Z}_2$ breaking,
tadpole-induced $\mathbb{Z}_2$ breaking, and quartic-induced $\mathbb{Z}_2$
breaking. We investigate the Higgs mass spectra and the Higgs phenomenology in
these scenarios.
