While numerous attempts have been made to jointly parse syntax and semantics, high performance in one domain typically comes at the price of performance in the other. This trade-off contradicts the large body of research focusing on the rich interactions at the syntax--semantics interface. We explore multiple model architectures that allow us to exploit the rich syntactic and semantic annotations contained in the Universal Decompositional Semantics (UDS) dataset, jointly parsing Universal Dependencies and UDS to obtain state-of-the-art results in both formalisms. We analyze the behavior of a joint model of syntax and semantics, finding patterns supported by linguistic theory at the syntax--semantics interface. We then investigate to what degree joint modeling generalizes to a multilingual setting, where we find similar trends across 8 languages.