Friedrichs’ systems are first order linear systems that allow to treat in a unified framework a large class of hyperbolic systems and mixed-form elliptic equation satisfying symmetry and positiviy assumptions. In [Ern, Guermond 2006], the authors present a unified analysis of existence and uniqueness of solutions of Friedrich’s systems in graph spaces and introduce a general DG scheme for their approximation. Inspired by these results, in this work we present a systematic analysis of inf-sup stability and h-convergence for a general hybrid scheme for stationary Friedrichs systems. The method features polynomial unknowns on both the elements and faces of the mesh. Hybridization allows to design arbitrary-order schemes that guarantee local balance properties and leads to a reduced computational cost thanks to the static condensation of element unknowns. For sufficiently smooth solutions, the method is proven to provide estimates of order h^k+1/2 in a graph-like norm controlling the L2 norm of the error and the directional derivative; the dependence of the estimates on the parameters of the problem is made explicit. The scheme can be seen as a generalization of the method proposed in [Chen, Kang et al., 2024], leveraging an upwind discretization of advective terms. We display numerical tests in which the method is adopted to approximate diffusion-advection-reaction equations in mixed form with scalar or vector unknowns.