The dorsal (DRN) and median (MRN) raphe are important nuclei implicated in sleep and mood regulation. The DRN is mainly serotonergic, where neurons have regular spiking activity, slow firing rate (FR), and long action potential duration (APD). The MRN has more diverse neurochemical and electrophysiological features. In the present study, we aimed to enrich the characterization of the raphe nuclei neurons by using non-linear measures. This was done by analysing the neuronal basal firing profile in both nuclei of urethane-anesthetized rats using Ordinal Patterns (OP) Entropy, Bins Entropy, and Permutation Lempel-Ziv Complexity (PLZC). In a first step, we found that typical measures -- such as FR, coefficient of variation (CV), and APD -- fail to distinguish between MRN and DRN neurons, while OP entropy is significantly different between these nuclei. We also found that the FR has a strong linear relationship with CV, Bins Entropy, and PLZC. Similarly, CV has a strong correlation with FR and Bins Entropy, whereas PLZC shows a strong linear fit with Bins Entropy. However, OP Entropy has either a weak or no linear relationship with the rest of the measures tested, suggesting that OP Entropy is a good measure to differentiate neuronal firing profiles. In a second step, we studied how these measures are affected by the oscillatory properties of the firing patterns. We found that all measures are sensitive to rhythmicity -- with the exception of OP Entropy. Again, this highlights OP Entropy as a powerful quantity for the characterization of neuronal discharge patterns.