Previous research suggests that statistical learning enhances memory for self-related information at the individual level and that individuals exhibit better memory for partner-related items than they do for irrelevant items in joint contexts (i.e., the joint memory effect, JME). However, whether statistical learning improves memory for partner-related information in joint contexts remains unclear. This study investigated memory performance for partner-related words when higher level statistical regularities were embedded in word streams during a joint memory task. Participants performed a word categorization task, followed by a surprise free recall task across four experiments. Experiment 1 replicated the JME, revealing improved memory for partner-related items than for irrelevant items when using Chinese words with increased repetition. Experiment 2 embedded semantic regularities within partners' word streams; Experiment 3a employed regularities based on non-adjacent fixed temporal positions; and Experiment 3b employed regularities based on adjacent fixed temporal positions. Results showed that the JME was enhanced only when semantic regularities were present (Experiment 2) and not with temporal positional rules (Experiments 3a and 3b). These findings suggest a hierarchical structure of co-representation and show that co-represented statistical regularities facilitate the processing of partner-related words, but only when the regularities align with partners' intentions. This study advances our understanding of co-representation in joint action by highlighting its hierarchical nature, and the top-down interaction between structural levels.