Semi-continuous data, also known as zero-inflated continuous data, have a substantial portion of responses equal to a single value (typically 0) and a continuous, right-skewed distribution among the remaining positive values. For jointly modeling multivariate clustered semi-continuous responses, the covariate effects in the positive parts can be proportionally constrained to the covariate effects in the logistic part, yielding a multivariate two-part fixed effects model. It is shown that, both theoretically and experimentally, the proportionally constrained model is more efficient than the unconstrained model in terms of parameter estimation, and thus provides a deeper understanding of the data structure when the proportionality structure holds. A robust variance estimation method is also introduced and tested under various model mis-specified cases. The proposed model is applied to data from a randomized controlled trial evaluating potential preventive effects of meditation or exercise on duration and severity of acute respiratory infection illness. The new analysis infers that meditation not only has highly significant effects on reduction of acute respiratory infection severity and duration, but also has significant effects on preventing acute respiratory infection, which was not previously reported in the literature.