Metal-organic framework (MOF)-based drug delivery nanosystems with both precise drug release and multidrug codelivery capabilities have emerged as promising candidates for cancer treatment. However, challenges are posed by the limited number of suitable payload types, uncontrollable drug leakage, and lack of chemical groups for postmodification. To overcome those challenges, we developed a core-shell nanocomposite composed of zeolitic imidazolate framework-90 (ZIF-90) coated with spermine-modified acetalated dextran (SAD) by a facile microfluidics-based nanoprecipitation method. This nanocomposite could serve as a multidrug storage reservoir for the loading of two drugs with distinct properties, where the hydrophilic doxorubicin (DOX) was coordinately attached to the ZIF-90 framework, and hydrophobic photosensitizer IR780 was loaded into the SAD shell, enabling the combination therapy of photodynamic treatment with chemotherapy. Meanwhile, equipping ZIF-90 with a SAD shell not only substantially improved the pH-responsive drug release of ZIF-90 but also enabled the postformation conjugation of ZIF-90 with hyaluronic acid for specific CD44 recognition, thereby facilitating precise drug delivery to CD44-overexpressed tumor. Such a simple microfluidics-based strategy can efficiently overcome the limitations of solely MOF-based DDSs and greatly extend the flexibility of MOF biomedical applications.