Optical imaging with single-pixel detection could not work well in some complex scenarios, when a single type of illumination patterns is applied. Here, we report on correspondence imaging (CI) with mixed illumination patterns to achieve high-quality object reconstruction and high robustness in complex environments with random disturbances. A series of mixed illumination patterns are generated to be displayed alternately, i.e., sinusoidal patterns and random patterns. The dynamic scaling factors induced by complex environments with random disturbances are estimated from the sequence of collected light intensities obtained when random patterns are used and then are applied to correct the sequence of collected light intensities obtained when sinusoidal patterns are used. The series of corrected light intensities is employed for an initial reconstruction, and an object image is finally recovered by using a physics-enhanced neural network (PENet) without the use of training data. It is illustrated in optical experiments that the proposed method achieves high robustness in complex environments with random disturbances, and the recovered object images are of high fidelity. The proposed method can open an avenue to establish high-performance CI systems in complex environments with random disturbances.