This paper proposes a hybrid multiband (MB) ultra wideband (UWB) system with direct sequence (DS) spreading. The theoretical error analysis for the DS-MB-UWB multiple access system with Rake receiver in the presence of multipath and narrowband interference is developed. The developed theoretical framework models the multiple access interference (MAI), multipath interference (MI) and narrowband interference for the designed UWB system. It is shown that the system error performance corresponding to the combining effects of these interference can be accurately modeled and calculated. Monte Carlo simulation results are provided to validate the accuracy of the model. Additionally, it is found that narrowband interference can be mitigated effectively in the multiband UWB system by suppressing the particular UWB sub-band co-existing with the interfering narrowband signal. A typical improvement of 5dB can be achieved with 75% sub-band power suppression. On the other hand, suppression of UWB sub-band is also found to decrease frequency diversity, thus facilitating the increase of MAI. In this paper, the developed model is utilized to determine the parameters that optimize the UWB system performance by minimizing the effective interference.