We considered the problem of constructing nonparametric confidence intervals for the difference in the means of two independent skewed populations which contain zero values. To account for zero values, we used a two-part model to separately estimate the probability of having any non-zero value and the expected value of positive observations. Under such a two-part model we developed the empirical likelihood (EL) based interval for the difference in the two population means. We then derived asymptotic properties of the proposed method. In a simulation study, we showed that the EL-based interval outperforms the existing normal approximation method and the bootstrap method. Finally, we illustrated the application of the proposed method in a study that assessed the relationship between the excess charges among older patients and the burden of their medical illness.