This paper proposes UniStream, a unified stream architecture based on point-to-point stream channels combining both bitstream configuration and data stream processing. In addition, unified APIs are provided to support bitstream configuration and data stream processing, as well as the stream interconnect. A cost model is also presented for the overhead on the stream interconnect, hardware task configuration and data stream processing at system level, which can be used during the early stage of development. The flexibility and high efficiency of UniStream are demonstrated on Xilinx Virtex-5 and Virtex-6 FPGAs. Experimental results on bitstream configuration/ read-back, data encryption/decryption and Discrete Cosine Transformation show that performance can be significantly improved with different stream modes.