The intelligent omni-surface (IOS) is a dynamic metasurface that has recently been proposed to achieve full-dimensional communications by realizing the dual function of anomalous reflection and anomalous refraction. Existing research works provide only simplified models for the reflection and refraction responses of the IOS, which do not explicitly depend on the physical structure of the IOS and the angle of incidence of the electromagnetic (EM) wave. Therefore, the available reflection-refraction models are insufficient to characterize the performance of full-dimensional communications. In this paper, we propose a complete and detailed circuit-based reflection-refraction model for the IOS, which is formulated in terms of the physical structure and equivalent circuits of the IOS elements, as well as we validate it against full-wave EM simulations. Based on the proposed circuit-based model for the IOS, we analyze the asymmetry between the reflection and transmission coefficients. Moreover, the proposed circuit-based model is utilized for optimizing the hybrid beamforming of IOS-assisted networks and hence improving the system performance. To verify the circuit-based model, the theoretical findings, and to evaluate the performance of full-dimensional beamforming, we implement a prototype of IOS and deploy an IOS-assisted wireless communication testbed to experimentally measure the beam patterns and to quantify the achievable rate. The obtained experimental results validate the theoretical findings and the accuracy of the proposed circuit-based reflection-refraction model for IOSs.