In this article, we propose a variant of reconfigurable intelligent surfaces (RISs) called omni-digital-RISs (omni-DRISs), which allows both light reflection and refraction, with application to indoor visible light communication systems. The omni-DRIS contains elements which can be either reflectors or refractors, or both simultaneously. We describe and explain the concept of omni-ORIS, suggest and analyze an omni-DRIS coding structure, discuss metamaterials to be used in the omni-DRIS module, and provide a design example. Furthermore, we demonstrate that the achievable rate of an omni-DRIS system depends on the number of omni-DRIS elements, bits per phase shift, and actively absorbing elements. In addition, we show that the upper bound of the achievable rate is related to the number of omni-ORIS elements, and conclude by discussing future research directions.