We discuss the phenomenology of charged Higgs bosons in the MSSM with minimal flavor violation. In addition to the constrained MSSM (CMSSM) with universal soft supersymmetry breaking mass parameters at the GUT scale, we explore non-universal Higgs mass models (NUHM) where this universality condition is relaxed. To identify the allowed parameter space regions, we apply constraints from direct searches, low energy observables, and cosmology. We find that values of the charged Higgs mass as low as m_H⁺ 135 GeV can be accommodated in the NUHM models, but that several flavor physics observables disfavor large H⁺ contributions, associated with high tan β, quite independently of MSSM scenario. We confront the constrained scenarios with the discovery potentials reported by ATLAS and CMS, and find that the current exclusion by indirect constraints is similar to the expected LHC discovery reach with 30 fb⁻¹ of data. Finally, we evaluate the sensitivity of the presented discovery potential to the choice of MSSM benchmark scenario. This sensitivity is found to be higher in the case of a light (m_H⁺ < m_t) charged Higgs.