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A new two-user cognitive radio channel model with partial knowledge of the primary messages at the cognitive transmitter is proposed in this paper. It is the combination of the interweave channel and the interference channel. The new channel model has two advantages. First, by introducing the switch concept, the spectrum sensing is combined to the channel model. Second, by introducing the compression theory, the cognitive transmitter (Tx1) can sense the partial knowledge of messages that is sent by the primary's transmitter (Tx2) to its corresponding receiver through a compression channel. Based on this new channel, the channel capacity is analyzed and calculated. Finally, simulation results illustrate the validity of the new channel model and the advantage of its capacity.