This article presents a novel framework for enhancing the integrity and availability of data stored on multi-cloud storage systems. The proposed technique leverages a combination of interleaving and Luby transform (LT) codes, specifically employing either ideal or robust soliton distribution during the LT encoding stage. The proposed technique is rigorously designed, incorporating data preparation facilitated by a cloud broker and culminating in the measurement of key performance indicators (KPIs). A central component of the framework is data processing, which involves interleaving followed by the LT encoding with soliton distribution selection. The performance of the proposed technique is evaluated through data integrity, data availability, and others. The results demonstrate that using the robust soliton distribution offers a pragmatic balance between computational efficiency and robust data integrity, particularly crucial in dynamic multi-cloud environments. Additionally, the proposed technique achieves a high level of data integrity of more than 0.97 and strong resilience with average data availability of 98%. However, further optimization is necessary to address storage overhead, retrieval time, and computational overhead. Despite these considerations, the framework remains significant, especially within the context of confidentiality, integrity, and availability for multi-cloud storage protection. The proposed technique underscores the potential of integrating interleaving and LT codes to revolutionize data storage and access within cloud environments, paving the way for future innovations in the field.