  We discuss complementarity of discovery reaches of heavier neutral Higgs
bosons and charged Higgs bosons at the LHC and the International Linear
Collider (ILC) in two Higgs doublet models (2HDMs). We perform a comprehensive
analysis on their production and decay processes for all types of Yukawa
interaction under the softly-broken discrete symmetry which is introduced to
avoid flavour changing neutral currents, and we investigate parameter spaces of
discovering additional Higgs bosons at the ILC beyond the LHC reach. We find
that the 500 GeV run of the ILC with the integrated luminosity of 500 fb^{-1}
shows an advantage for discovering the additional Higgs bosons in the region
where the LHC cannot discover them with the integrated luminosity of 300
fb^{-1}. For the 1 TeV run of the ILC with the integrated luminosity of 1
ab^{-1}, production processes of an additional Higgs boson associated with the
top quark can be useful as discovery channels in some parameter spaces where
the LHC with the integrated luminosity of 3000 fb^{-1} cannot reach. It is
emphasized that the complementary study at the LHC and the ILC is useful not
only to survey additional Higgs bosons at the TeV scale, but also to
discriminate types of Yukawa interaction in the 2HDM.
