In this paper, we consider bidirectional relaying between two diffusion-based molecular transceivers (bio-nodes). As opposed to existing literature, we incorporate the effect of direct diffusion links between the nodes and leverage it to improve performance. Assuming network coding type operation at the relay, we devise a detection strategy, based on the maximum-likelihood principle, that combines the signal received from the relay and that received from the direct link. At the same time, since a diffusion-based molecular communication channel is characterized by high inter-symbol interference (ISI), we utilize a decision feedback mechanism to mitigate its effect. Simulation results indicate that the proposed setup incorporating the direct link can achieve notable improvement in error performance over conventional detection schemes that do not exploit the direct link and/or do not attempt to mitigate the effect of ISI.