This paper examines the features of a generalized position-dependent mass Hamiltonian Hm in a supersymmetric framework in which the constraints of pseudo-Hermiticity and [formula omitted] are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials [formula omitted] which are inherently [formula omitted]-symmetric. The qualitative spectral behavior of Hm is studied and several interesting consequences are noted. © 2013, American Institute of Physics. All rights reserved.