The CY4601 USB to Serial driver supports full duplex.However, the CY7C63743 and CY7C64013 firmware do not support full duplex. These two parts only support half duplex due to the limited bandwidth of the part.
The serial interface is bit banged and therefore the bits need to be transmitted and received (sampled) in a very deterministic behavior, otherwise they will get out of sync. Under full duplex, the current code base may get thrown out of sync while sampling incoming data or transmitting outgoing data. Developers may be able to customize this reference design for full duplex, but only under controlled applications where the data patterns are known.
Please find attached the sample code for CY4601.