Heritage language (HL) speakers seem to diverge from monolingual speakers in the acquisition of syntax–discourse interface phenomena. However, most of the studies reporting this finding do not make any distinction between different types of syntax–discourse interface structures. Therefore, it is an open question whether these structures are difficult for HL speakers across the board or whether different types of structures are associated with different acquisition outcomes. In this study, we investigate whether the timing of the acquisition of syntax–discourse interface structures among monolingual children affects their acquisition by HL children. We consider the acquisition of the alternation between preverbal and postverbal subjects with unaccusative, unergative and transitive verbs in Italian. This alternation involves the syntax–discourse interface across all verb types. However, mastery of this alternation has a different timing in monolingual acquisition depending on the verb type: it emerges earlier in association with unaccusative verbs than unergative and transitive ones. We elicit narratives in Italian from 42 Italian heritage children living in Germany and ranging in age from 7 to 14 years. We focus on the analysis of preverbal and postverbal subjects, considering the effect of verb type and discourse status of the subject. The children show a good mastery of the alternation between preverbal and postverbal subjects with unaccusative verbs, whereas they exhibit difficulties with the same alternation in association with transitive and unergative verbs. Furthermore, postverbal subjects with transitive verbs are particularly vulnerable to cross-linguistic effects from German. The results of the study suggest a gradient interpretation of heritage speakers’ difficulty with syntax–discourse interface structures, with timing in monolingual acquisition being a relevant factor that modulates the degree of this difficulty. The results are not affected by children’s dominance of exposure to Italian or age.