This paper introduces μ-NET, a microfluidic LAN that supports the exchange of both digital information and biochemical information carried by droplets moving across molecular processors in a microfluidic chip. The μ-NET can be used to support molecular biology applications like DNA, RNA, and protein biosynthesis. The μ-NET is the first realization of a microfluidic networking paradigm that controls movements of droplets in microfluidic chips by exploiting hydrodynamic phenomena only and builds on recent solutions to achieve communications in the microfluidic domain. The μ-NET integrates techniques to represent addressing information, as well as switching and medium access control solutions. In fact, in μ-NET, the address of the molecular processor where a droplet should be sent to is encoded into the distance between droplets; switching is executed to steer the droplets inside the microfluidic device; medium access control is applied to avoid collisions between droplets that may result in their fusion and, thus, loss of the biochemical information. In this paper, the design of μ-NET is presented in detail, and simulation results validating μ-NET operations are shown.