The electromagnetic continuity condition is extended from the classical condition on an interface between two media to a more general one relating sources and fields in a region between two regions of arbitrary media. The condition allows one to extend the classical Huygens principle to involve equivalent sources in a spatial region volume or on multiple surfaces. As an example, the generalized Huygens principle is applied to the formulation of a scattering problem in terms of a surface integral equation. Also, the transparent absorbing boundary (TAB) condition can be interpreted in terms of the extended Huygens principle.