In a multiple-input multiple-output (MIMO), multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) system, coherent detection requires the transmission of a large number of symbols for channel estimation, thus reducing the bandwidth efficiency. For the first time, this paper proposes unitary differential space-time-frequency codes (DSTFCs) for MB-OFDM UWB communications, which increase the system bandwidth efficiency because no channel state information (CSI) is required. The proposed system would be useful when CSI is unavailable at the receiver, such as when the transmission of multiple channel estimation symbols is impractical or uneconomical. The coding and decoding algorithms for the proposed DSTFCs are then derived for both constant envelope modulation scheme, such as PSK (phase shift keying) and 4QAM (quadrature amplitude modulation), and multi-dimensional modulation scheme, such as DCM (dual carrier modulation). The paper also quantifies for the first time the diversity order of a DSTFC MB-OFDM system. Simulation results show that the application of DSTFCs can significantly improve the bit error performance of conventional differential MB-OFDM system (without MIMO), and even provide much better bit error performance than the conventional coherent MB-OFDM system (without MIMO) at high signal-to-noise ratios.