We discuss the properties of the Standard Model-like Higgs boson in the pMSSM, a 19/20 – dimensional parameter space that captures most of the relevant phenomenology of the general MSSM. Within this framework, we characterize the range of possible deviations in the Higgs couplings to standard model particles and examine the possibility of invisible Higgs decays. We show that precision Higgs coupling measurements at the 14 TeV LHC and at the proposed 500 GeV ILC will be sensitive to many pMSSM models which are allowed by current data, including models which are expected to remain allowed after the 14 TeV LHC SUSY searches. In particular, we see that most of our models predict SUSY corrections to the h-g-g and h-b-b couplings that will be observable with future experimental precision. We also show that the null results of current LHC SUSY searches have a very mild effect on the distributions of possible Higgs couplings within our model set.