Optical diffraction tomography (ODT) is an important technique for three-dimensional (3D) imaging of semi-transparent biological samples, enabling volumetric visualization of living cells, cultures, and tissues without the need for exogenous dyes. However, ODT faces significant challenges in imaging complex biological specimens due to the limited specificity of refractive index (RI) and the coupled relationship between absorption and phase in image formation. Here, we present multi-modal transport of intensity diffraction tomography (MM-TIDT), a high-speed 3D microscopy technique that integrates an electrically tunable lens with modified illumination patterns to decouple phase and absorption information. Leveraging dual illumination schemes-circular and annular apertures-MM-TIDT acquires two intensity stacks, facilitating accurate phase and absorption decoupling. Based on an alternating direction method of multipliers (ADMM) framework with total variation (TV) and non-negativity regularization, our method reconstructs multi-modal 3D distributions of fluorescence and complex RI with high accuracy and robustness. Experimental validation with fluorescent polystyrene microspheres, Spirulina specimens, and DAPI-labeled C166 cells demonstrates the multi-modal imaging capability of MM-TIDT to resolve fine structural details across diverse sample types, providing a versatile platform for exploring dynamic biological processes and intricate cellular interactions.