When people interact, aspects of their speech and language patterns often converge in interactions involving one or more languages. Most studies of speech convergence in conversations have examined monolingual interactions, whereas most studies of bilingual speech convergence have examined spoken responses to prompts. However, it is not uncommon in multilingual communities to converse in two languages, where each speaker primarily produces only one of the two languages. The present study examined complexity matching and lexical matching as two measures of speech convergence in conversations spoken in English, Spanish, or both languages. Complexity matching measured convergence in the hierarchical timing of speech, and lexical matching measured convergence in the frequency distributions of lemmas produced. Both types of matching were found equally in all three language conditions. Taken together, the results indicate that convergence is robust to monolingual and bilingual interactions because it stems from basic mechanisms of coordination and communication.