The paper extends existing models for multilevel multivariate data with mixed response types to handle quite general types and patterns of missing data values in a wide range of multilevel generalized linear models. It proposes an efficient Bayesian modelling approach that allows missing values in covariates, including models where there are interactions or other functions of covariates such as polynomials. The procedure can also be used to produce multiply imputed complete data sets. A simulation study is presented as well as the analysis of a longitudinal data set. The paper also shows how existing multiprocess models for handling endogeneity can be extended by the framework proposed. © 2013 Royal Statistical Society.