The Partially asymmetric exclusion process (PASEP) is a physical model viewed as a Markov chain representing the displacement of particles over a finite line. The steady-state probabilities of this chain can be computed by enumerating permutations according to certain statistics. These probabilities have a natural connexion with some transition matrices, in the algebra of noncommutative symmetric functions, which implies a refinement of the probabilities of the PASEP using statistics on permuations. We place ourself in the context of the 2-PASEP, the PASEP with two kind of particles, and exhibit a connexion with the free algebra indexed by segmented compositions using statistics on partially signed permutations.