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, m
2
Hu,d
, vary independently from the universal soft SUSY-breaking contributions m
2
0
to the masses of squarks and sleptons. Our analysis uses the MultiNest sampling algorithm with over 4×108 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 + /ET signals using the full LHC Run 1 data, the measurements of BR(Bs→μ+μ−) 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, m
2
0
<0, as well as m
2
Hu
<m
2
Hd
<0. The tension present in the CMSSM and NUHM1 between the supersymmetric interpretation of (g−2)μ and the absence to date of SUSY at the LHC is not significantly alleviated in the NUHM2. We find that the minimum χ2=32.5 with 21 degrees of freedom (dof) in the NUHM2, to be compared with χ2/dof=35.0/23 in the CMSSM, and χ2/dof=32.7/22 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.