Cloud-assisted e-healthcare sharing systems (EHSSs) play an increasingly pivotal role in the contemporary healthcare field. By outsourcing electronic medical records (EMRs) to the cloud, hospitals can alleviate local storage and management burdens while facilitating data sharing. Due to the highly sensitive nature of EMRs, encryption is necessary before storing them on the cloud. Attribute-based keyword search (ABKS) enables the privacy protection of EMRs with efficient search services. However, there remain some limitations in practical application. Firstly, most ABKS schemes only support single keyword queries, resulting in inaccurate results and wastage of computing and bandwidth resources. Secondly, since sensitive information within EMRs is encrypted as a whole, different data users (including internal doctors and external researchers) should have varying access rights to prevent leakage of this sensitive information. Thirdly, incorrect search results could lead to misdiagnosis or endanger patients' lives and affect researchers' decision-making processes. To effectively tackle these challenges, this paper proposes a verifiable attribute-based multi-keyword search scheme with sensitive information hiding (VABMKS-SIH) for cloud-assisted EHSSs, where we present a secure model for multi-keyword search with two-level access structure by incorporating an improved blindness filtering technique into ciphertext-policy attribute-based encryption (CP-ABE) within existing keyword search framework. Our scheme employs a super-increasing sequence to aggregate multiple filtered data blocks into one unified ciphertext, thereby greatly reducing communication overhead during the transmission phases of ciphertext. To check the correctness of returned results, we introduce a lightweight algebraic signature algorithm based on fundamental algebraic operations. A security analysis demonstrates that VABMKS-SIH is provably secure under the random oracle mode. Additionally, we also evaluate the proposed scheme's performance to demonstrate its utility in cloud-assisted EHSSs.