In a large class of models, a light dark sector involving a dark Higgs singlet couples to the SM Higgs field through the portal coupling. Light ALPs (or hidden photons) predicted in these models can be viable candidates of dark matter, and may be produced via the decays of the SM Higgs boson and the (newly introduced) dark Higgs boson. Interestingly, these models exhibit similar properties and a search for invisible decays of the SM/dark Higgs boson may serve as a tool for a generic probe of all the scenarios. In this talk, after a brief introduction of the theoretical framework, I will discuss how we can probe the light dark sector by performing a search for invisible decays of the SM and dark Higgs bosons at the International Linear Collider (ILC). Taking account of both the Higgs bosons in this search offers a golden opportunity to extend the probe of the dark sector to regions a few orders of magnitude below the planned reach of the ILC for invisible decays of the SM Higgs boson.