Methods for causal inference with binary treatment have recently been extended to deal with continuous exposures. In many settings however, including our motivating study on the effects of prenatal alcohol exposure on child cognition, the exposure distribution is semi-continuous with a mass at zero with a sub-density characterizing exposure levels among exposed individuals. We develop a two-stage approach for modeling the causal effects of a semi-continuous exposure. In the first stage, the causal effect of the level of exposure is assessed among exposed individuals via a propensity score regression adjustment. In the second stage, the causal effect of the binary exposure is assessed via inverse probability weighted (IPW) and augmented inverse probability weighted (AIPW). We derive the large sample properties of the resulting estimators and construct joint confidence intervals for the causal effects. Simulation studies confirm good finite sample performance of the proposed estimators.