  We present in detail the bosonization-refermionization solution of the
anisotropic version of the two-channel Anderson model at a particular manifold
in the space of parameters of the theory, where we establish an equivalence
with a Fermi-Majorana bi-resonant level model. The correspondence is rigorously
proved by explicitly constructing the new fermionic fields and Klein factors in
terms of the original ones and showing that the commutation properties between
original and new Klein factors are of semionic type. We also demonstrate that
the fixed points associated to the solvable manifold are renormalization-group
stable and generic, and therefore representative of the physics of the original
model. The simplicity of the solution found, allows for the computation of the
full set of thermodynamic quantities. In particular, we compute the entropy,
occupation and magnetization of the impurity as functions of temperature, and
identify the different physical energy scales. In absence of external fields,
two energy scales appear and, as the temperature goes to zero, a non-trivial
residual entropy indicates that the model approaches a universal line of fixed
points of non-Fermi liquid type. An external field, even if small, introduces a
third energy scale and causes the quenching of the impurity entropy to zero,
taking the system to a corresponding Fermi-liquid fixed point.
