  We study black holes in the recently proposed ghost-free theory with two
gravitons, one of which is massive and another is massless. These black holes
possess a regular event horizon which is common for both metrics and has the
same values of the surface gravity and Hawking temperature with respect to each
metric. The ratio of the event horizon radii measured by the two metrics is a
free parameter that labels the solutions. We present a numerical evidence for
their existence and find that they comprise several classes. Black holes within
each class approach the same AdS-type asymptotic at infinity but differ from
each other in the event horizon vicinity where the short-range massive modes
reside. In addition, there are solutions showing a curvature singularity at a
finite proper distance from the horizon. For some special solutions the
graviton mass may become effectively imaginary, causing oscillations around the
flat metric at infinity. The only asymptotically flat black hole we find -- the
Schwarzschild solution obtained by identifying the two metrics -- seems to be
exceptional, since changing even slightly its horizon boundary conditions
completely changes the asymptotic behavior at infinity. We also construct
globally regular solutions describing `lumps of pure gravity' which can be
viewed as black hole remnants in the limit where the event horizon shrinks.
Finally, adding a matter source we obtain globally regular and asymptotically
flat solutions exhibiting the Vainstein mechanism of recovery of General
Relativity in a finite region.
