Conventional methods for mediation analysis generate biased results when the mediator--outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator interactions. The indirect effect can be further decomposed into a pure indirect effect and a natural treatment-by-mediator interaction effect. Similar to other techniques for causal mediation analysis, RMPW generates causally valid results when the sequential ignorability assumptions hold. Yet unlike the model-based alternatives, including path analysis, structural equation modeling, and their latest extensions, RMPW requires relatively few assumptions about the distribution of the outcome, the distribution of the mediator, and the functional form of the outcome model. Correct specification of the propensity score models for the mediator remains crucial when parametric RMPW is applied. This article gives an intuitive explanation of the RMPW rationale, a mathematical proof, and simulation results for the parametric and nonparametric RMPW procedures. We apply the technique to identifying whether employment mediated the relationship between an experimental welfare-to-work program and maternal depression. A detailed delineation of the analytic procedures is accompanied by online Stata code as well as a stand-alone RMPW software program to facilitate users' analytic decision making.