Zero-shot cross-lingual information extraction(IE) aims at constructing an IE model for some low-resource target languages, given annotations exclusively in some rich-resource languages. Recent studies based on language-universal features have shown their effectiveness and are attracting increasing attention. However, prior work has neither explored the potential of establishing interactions between language-universal features and contextual representations nor incorporated features that can effectively model constituent span attributes and relationships between multiple spans. In this study, a syntax-augmented hierarchical interactive encoder (SHINE) is proposed to transfer cross-lingual IE knowledge. The proposed encoder is capable of interactively capturing complementary information between features and contextual information, to derive language-agnostic representations for various IE tasks. Concretely, a multi-level interaction network is designed to hierarchically interact the complementary information to strengthen domain adaptability. Besides, in addition to the well-studied syntax features of part-of-speech and dependency relation, a new syntax feature of constituency structure is introduced to model the constituent span information which is crucial for IE. Experiments across seven languages on three IE tasks and four benchmarks verify the effectiveness and generalization ability of the proposed method.