In ambient backscatter communications, backscatter devices (BDs) utilize ambient “legacy” radio signals as both a harvested energy source and a carrier on which to modulate data. Symbiotic radio, a subtype in which the legacy system assists both its own users and underlaid BDs, has attracted much research interest recently. Furthermore, cell-free massive multiple-input multiple-output (CF mMIMO) systems are promising for beyond-5G networks from both spectral and energy efficiency perspectives. To reap the benefits of both, we consider a primary CF mMIMO system where the access points (APs) aid an underlaid BD layer to both harvest energy and reflect information toward the primary receivers (which receive data from both layers). To acquire separate channel state information (CSI) of the direct and backscattered channels at the APs, a two-phase uplink pilot training method is proposed, with the effects of pilot contamination and spatial correlation between antennas accounted for. However, the receivers are assumed to only have partial CSI (statistical knowledge plus instantaneous phase information for partially-coherent reception). Assuming uplink/downlink radio channel reciprocity, the CSI is used to design downlink precoding vectors for the APs such that channel hardening is enhanced and both primary receivers and BDs benefit. We derive expressions for the average signal-to-interference-plus-noise ratios of both primary and backscatter signals, accounting for the effects of imperfect CSI, spatial correlation, pilot contamination, and channel hardening. Furthermore, the average power harvested in the BDs is derived. Simulation results demonstrate that the performance of the proposed scheme is much more uniform across all devices with CF mMIMO than with conventional co-located mMIMO. The use of CF mMIMO also largely removes the need for special consideration of the BD layer in the symbiotic system, which is not the case with co-located mMIMO.