Intelligent omni-surfaces (IOS) have attracted great attention recently due to its potential to achieve full-dimensional communications by simultaneously reflecting and refracting signals toward both sides of the surface. However, it still remains an open question whether the reciprocity holds between the uplink and downlink channels in the IOS-aided wireless communications. In this work, we first present a physics-compliant IOS related channel model, based on which the channel reciprocity is investigated. We then demonstrate the angle-dependent electromagnetic response of the IOS element in terms of both incident and departure angles. This serves as the key feature of IOS that drives our analytical results on beam non-reciprocity. Finally, simulation and experimental results are provided to verify our theoretical analyses.