We report on a new class of solutions of black hole accretion disks that we have found through three-dimensional, global, radiative magnetohydrodynamic simulations in general relativity. It combines features of the canonical thin, slim, and thick disk models but differs in crucial respects from each of them. We expect these new solutions to provide a more realistic description of black hole disks than the slim disk model. We are presenting a disk solution for a nonspinning black hole at a sub-Eddington mass accretion rate, Mdot = 0.6 Mdot_Edd. By the density scale-height measure the disk appears to be thin, having a high density core near the equatorial plane of height h_rho ~ 0.1 r, but most of the inflow occurs through a highly advective, turbulent, optically thick, Keplerian region that sandwiches the core and has a substantial geometrical thickness comparable to the radius, H ~ r. The accreting fluid is supported above the midplane in large part by the magnetic field, with the gas and radiation to magnetic pressure ratio beta ~ 1, this makes the disk thermally stable, even though the radiation pressure strongly dominates over gas pressure. A significant part of the radiation emerging from the disk is captured by the black hole, so the disk is less luminous than a thin disk would be at the same accretion rate.