It is a rigorous task to jointly analyze mixed ordinal and continuous data, especially with substantial missing values, due to the complicated correlated structure of those mixed data and nonidentifiability induced by variance parameters (such as in joint mixed effect models). Also, the identifiable multivariate probit model requires the variances of the latent normal variables fixed at 1, thus the joint covariance matrix of the latent variables and the continuous multivariate normal variables is restricted at some of the diagonal elements which are fixed at 1. This hinders to develop efficient Markov chain Monte Carlo (MCMC) sampling methods. In this investigation, we propose a parameter-expanded data augmentation to analyze mixed ordinal and continuous data with missing values by assuming multivariate probit model for ordinal data and continuous variables following multivariate normal distributions. By introducing redundant variance parameters our algorithm shows that the convergence and mixing of the MCMC sampling components exceed those based on the identifiable model. We illustrate our method through simulation studies and a real data application.