  In this work, we study the junction conditions of the ghost-free subclass of
quadratic Poincar\'e Gauge gravity, which propagates one scalar and one
pseudo-scalar. For this purpose, we revisit the theory of distributions and
junction conditions in gravity, giving a novel insight to the subject by
introducing a convenient notation to deal with regular and singular parts.
Then, we apply this formalism to bi-scalar Poincar\'e Gauge gravity and study
some paradigmatic cases. We compare our results with the existing literature
and the well-known predictions of General Relativity. We find that monopole
spin densities are admissible, whereas both thin shells and double layers are
allowed for the energy-momentum. Such layers can be avoided by setting
appropriate continuity conditions on the dynamic fields of the theory, as well
as on the Ricci scalar of the full connection and the Holst pseudo-scalar.
