This paper proposes a cognitive interference-mitigation technique for a hybrid direct sequence (DS) multiband (MB) ultra wideband (UWB) system. Theoretical framework of the DS-MB-UWB multiple access system employing cognitive interference-detection and mitigation is constructed over multipath environment in the presence of a coexisting narrowband wireless system. Interference mitigation is achieved through partially suppressing the power of the particular sub-band coexisting with the narrowband signal. A typical error performance improvement of around 10 fold can be achieved by suppressing 75% power of the affected sub-band. Additionally, increasing the number of sub- bands is found to achieve more improvement than increasing the number of DS chips. This paper attempts to develop a cognitive mitigation technology able to obtain optimum performance improvement while maintaining the highest possible frequency diversity.