We make a frequentist analysis of the parameter space of the NUHM2, in which the soft supersymmetry (SUSY)-breaking contributions to the masses of the two Higgs multiplets, [Formula: see text], vary independently from the universal soft SUSY-breaking contributions [Formula: see text] to the masses of squarks and sleptons. Our analysis uses the MultiNest sampling algorithm with over [Formula: see text] points to sample the NUHM2 parameter space. It includes the ATLAS and CMS Higgs mass measurements as well as the ATLAS search for supersymmetric jets + [Formula: see text] signals using the full LHC Run 1 data, the measurements of [Formula: see text] by LHCb and CMS together with other B-physics observables, electroweak precision observables and the XENON100 and LUX searches for spin-independent dark-matter scattering. We find that the preferred regions of the NUHM2 parameter space have negative SUSY-breaking scalar masses squared at the GUT scale for squarks and sleptons, [Formula: see text], as well as [Formula: see text]. The tension present in the CMSSM and NUHM1 between the supersymmetric interpretation of [Formula: see text] and the absence to date of SUSY at the LHC is not significantly alleviated in the NUHM2. We find that the minimum [Formula: see text] with 21 degrees of freedom (dof) in the NUHM2, to be compared with [Formula: see text] in the CMSSM, and [Formula: see text] in the NUHM1. We find that the one-dimensional likelihood functions for sparticle masses and other observables are similar to those found previously in the CMSSM and NUHM1.