A lensless camera is an ultra-thin computational-imaging system. Existing lensless cameras are based on the axial arrangement of an image sensor and a coding mask, and therefore, the back side of the image sensor cannot be captured. In this paper, we propose a lensless camera with a novel design that can capture the front and back sides simultaneously. The proposed camera is composed of multiple coded image sensors, which are complementary-metal-oxide-semiconductor~(CMOS) image sensors in which air holes are randomly made at some pixels by drilling processing. When the sensors are placed facing each other, the object-side sensor works as a coding mask and the other works as a sparsified image sensor. The captured image is a sparse coded image, which can be decoded computationally by using compressive-sensing-based image reconstruction. We verified the feasibility of the proposed lensless camera by simulations and experiments. The proposed thin lensless camera realizes super field-of-view imaging without lenses or coding masks, and therefore can be used for rich information sensing in confined spaces. This work also suggests a new direction in the design of CMOS image sensors in the era of computational imaging.