  A mixed spin-electron model on decorated planar lattices formed by
corner-sharing trigonal bipyramids is exactly solved by imposing three mobile
electrons per triangular cluster of each bipyramid by means of a generalized
decoration-iteration mapping transformation. It is shown that the ground state
of the model involves two spontaneously long-range ordered phases, namely, the
classical phase with a perfect ferromagnetic arrangement of all particles and
the macroscopically degenerate quantum one. The macroscopic degeneracy of the
quantum phase lies in chiral degrees of freedom of the mobile electrons.
Finite-temperature phase diagrams as well as temperature variations of the
spontaneous magnetization, entropy, and specific heat clearly prove that the
classical spin-electron arrangement is thermally almost twice more stable than
the quantum one for some combinations of the model's parameters.
