Cell-free massive MIMO and symbiotic radio communication have been recently proposed as the promising beyond fifth-generation (B5G) networking architecture and transmission technology, respectively. To reap the benefits of both, this paper studies cell-free symbiotic radio communication systems, where a number of cell-free access points (APs) cooperatively send primary information to a receiver, and simultaneously support the passive backscattering communication of the secondary backscatter device (BD). We first derive the achievable communication rates of the active primary user and passive secondary user under the assumption of perfect channel state information (CSI), based on which the transmit beamforming of the cellfree APs is optimized to characterize the achievable rate-region of cell-free symbiotic communication systems. Furthermore, to practically acquire the CSI of the active and passive channels, we propose an efficient channel estimation method based on two-phase uplink-training, and the achievable rate-region taking into account CSI estimation errors are further characterized. Simulation results are provided to show the effectiveness of our proposed beamforming and channel estimation methods.