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, $m^2_{H_{u,d}}$, 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 $4 times 10^8$ points to sample the NUHM2 parameter space. It includes the ATLAS and CMS Higgs mass measurements as well as their searches for supersymmetric jets + MET signals using the full LHC Run~1 data, the measurements of $B_s to mu^+ mu^-$ 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 for squarks and sleptons, $m_0^2 < 0$, as well as $m^2_{H_u} < m^2_{H_d} < 0$. The tension present in the CMSSM and NUHM1 between the supersymmetric interpretation of $g_mu - 2$ and the absence to date of SUSY at the LHC is not significantly alleviated in the NUHM2. We find that the minimum $chi^2 = 32.5$ with 21 degrees of freedom (dof) in the NUHM2, to be compared with $chi^2/{rm dof} = 35.0/23$ in the CMSSM, and $chi^2/{rm dof} = 32.7/22$ 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.
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