We introduce a new method to tag Multiword Expressions (MWEs) using a linguistically interpretable language-independent deep learning architecture. We specifically target discontinuity, an under-explored aspect that poses a significant challenge to computational treatment of MWEs. Two neural architectures are explored: Graph Convolutional Network (GCN) and multi-head self-attention. GCN leverages dependency parse information, and self-attention attends to long-range relations. We finally propose a combined model that integrates complementary information from both, through a gating mechanism. The experiments on a standard multilingual dataset for verbal MWEs show that our model outperforms the baselines not only in the case of discontinuous MWEs but also in overall F-score.