  We study a bi-metric scalar-tensor gravity theory, invariant under disformal
transformations, describing how matter and gravitational fields respectively
propagate through spacetime. We show that the no-hair theorem for scalar-tensor
theories can be evaded, and we find hairy black hole solutions in the presence
of an electric charge that admits AdS, flat or dS asymptotics with spherical,
flat, or hyperbolic base manifolds. Spherically symmetric, asymptotically flat
black holes and asymptotically AdS configurations with any horizon topology are
compatible with a regular scalar field on and outside the event horizon. The
latter presents a rich thermodynamic behavior induced by the disformal factor
that enters as a coupling parameter in the theory. In the grand canonical
ensemble, there is an interplay of stability and first-order phase transitions
between thermal AdS, the hairy black hole, and the Reissner-Nordstr\"om-AdS
black hole, whose thermodynamic phase space resembles a solid-liquid-gas
system, with an electric potential playing the role of pressure. In close
analogy, there is a triple point where the three phases coexist, being equally
probable.
