Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. Optical frequency combs can replace the multiple lasers used for the different wavelength channels. Beyond multiplexing, it has been suggested that the broadband phase coherence of frequency combs could simplify the receiver scheme by performing joint reception and processing of several wavelength channels, but an experimental validation in a fiber transmission experiment remains elusive. Here we demonstrate and quantify joint reception and processing of several wavelength channels in a full transmission system. We demonstrate two joint processing schemes; one that reduces the phase-tracking complexity and one that increases the transmission performance.