Quantitative phase microscopy (QPM) is a label-free imaging technique often employed for long-term, high-contrast imaging of live bio-samples. Yet, QPM is not specific to a certain subcellular organelle. As a remedy, fluorescence microscopy can visualize specific subcellular organelles once being labeled with fluorescent markers. In this paper, a high-resolution phase/fluorescence dual-modality microscopic imaging method based on structured light illumination is proposed. In a dual-modality microscopic system, periodic stripes are generated by a digital micromirror array (DMD), and are used as the common illumination for both modalities. For QPM imaging, the holograms of the sample under structured light illuminations from different directions and phase shifts are recorded, from which a quantitative phase image with resolution enhancement can be reconstructed via a synthetic aperture procedure. Furthermore, a numerical approach is proposed to compensate for the environmental disturbances that often challenge aperture synthesis of phase imaging. This method determines each time the phase distortions caused by environmental disturbances through using the spectrum of the 0th order of the structured light illumination, and the phase distortions are removed from the phase distributions of the waves along the 0th and the ±1st diffraction orders. Resolution enhancement of QPM imaging is realized by synthesizing the spectra of all the waves along different diffraction orders of the structured light illuminations of different orientations. With phase images, three-dimensional shapes, inner structures, or refractive index distributions of transparent and translucent samples can be obtained. For fluorescence imaging, intensity images (morie patterns) of the sample under different structured light illuminations are recorded. The spectra along different diffraction orders are separated by using a phase shifting reconstruction algorithm, and are shifted to their original positions, forming a synthesized spectrum that is much broader than the spectra of raw intensity images (NA-limited spectra). An inverse Fourier transform on the synthesized spectrum yields a super-resolution fluorescence image of the sample. With the reconstructed fluorescence images, specific subcellular organelles labeled with fluorescent markers can be visualized. The combination of quantitative phase microscopy and fluorescence microscopy can obtain multidimensional information about the sample. In this dual-mode imaging system, the spatial resolution of quantitative phase imaging and fluorescence imaging are 840 nm and 440 nm, respectively. The proposed dual-mode microscopy imaging technique has been demonstrated for imaging fluorescent beads, fly wings, spring/rice leaves, mouse tail transection, and fluorescence-stained SiHa cells. We envisage that this method can be further applied to many fields, such as biomedicine, industry, and chemistry.