Missing data is a common occurrence in confirmatory factor analysis (CFA). Much work had evaluated the performance of different techniques when all observed variables were either continuous or ordinal. However, few have investigated these techniques when observed variables are a mix of continuous and ordinal variables. This study investigated the performance of four approaches to handling missing data in these models: a joint ordinal-continuous full information maximum likelihood (FIML) approach and three multiple imputation approaches (fully conditional specification, fully conditional specification with latent variable formulation, and expectation-maximization with bootstrapping) combined with the weighted least squares with mean and variance adjustment (WLSMV) estimator. In a Monte-Carlo simulation, the FIML approach produced unbiased estimations of factor loadings and standard errors in almost all conditions. Fully conditional specification combined with WLSMV was second best, producing accurate estimates when the sample size was large. However, FIML encountered slight non-convergence issues when certain ordinal categories have extremely low frequencies, which is typical of skewed data. If the sample is large, fully conditional specification combined with weighted least squares is recommended when the FIML approach is not feasible (e.g., non-convergence, impractical computation durations, and variables that predict missingness are not of interest to the analysis).