We present dual-mode phase and fluorescence imaging in a confocal laser scanning microscopy (CLSM) system. For phase imaging, the depth of field of the CLSM system is extended by fast axial scanning with a tunable acoustic gradient index of refraction lens. Under transillumination, intensity images of the sample are recorded at a few different defocusing distances. The phase image is reconstructed from these intensity images by using the transport-of-intensity equation. The 3D fluorescence image is obtained by confocal scanning. The dual-mode images with pixel-to-pixel correspondence yield complementary quantitative structural and functional information. Combination of the two imaging modalities enables standalone determination of the refractive index of live cells.