The conventional single-target Cross-Domain Recommendation (CDR) aims to improve the recommendation performance on a sparser target domain by transferring the knowledge from a source domain that contains relatively richer information. By contrast, in recent years, dual-target CDR has been proposed to improve the recommendation performance on both domains simultaneously. However, to this end, there are two challenges in dual-target CDR: (1) how to generate both relevant and diverse augmented user representations, and (2) how to effectively decouple domain-independent information from domain-specific information, in addition to domain-shared information, to capture comprehensive user preferences. To address the above two challenges, we propose a Disentanglement-based framework with Interpolative Data Augmentation for dual-target Cross-Domain Recommendation, called DIDA-CDR. In DIDA-CDR, we first propose an interpolative data augmentation approach to generating both relevant and diverse augmented user representations to augment sparser domain and explore potential user preferences. We then propose a disentanglement module to effectively decouple domain-specific and domain-independent information to capture comprehensive user preferences. Both steps significantly contribute to capturing more comprehensive user preferences, thereby improving the recommendation performance on each domain. Extensive experiments conducted on five real-world datasets show the significant superiority of DIDA-CDR over the state-of-the-art methods.