Future wireless systems are supposed to provide high-resolution sensing services via communication signals. Under this background, multiband sensing has recently become a promising technology due to that it can improve the sensing performance by jointly utilizing multiple non-contiguous frequency bands at a low cost. However, few studies have investigated the fundamental limits of multiband sensing, especially in the presence of phase distortion factors. In this paper, we investigate the fundamental limits of multiband sensing in terms of time delay. We derive a closed-form expression of the Cramér-Ran bound (CRB) for the delay separation to reveal useful insights. Additionally, a metric called the statistical resolution limit (SRL) is employed to investigate the fundamental limits of delay resolution. The fundamental limits of delay estimation error are also investigated based on the CRB and Ziv-Zakai bound (ZZB). Based on the above derived fundamental limits, numerical results are presented to provide key insights on the performance limits of the multiband sensing.