Many surveys collect information on discrete characteristics and continuous variables, that is, mixed-type variables. Small-area statistics of interest include means or proportions of the response variables as well as their domain means, which are the mean values at each level of a different categorical variable. However, item nonresponse in survey data increases the complexity of small-area estimation. To address this issue, we propose a multivariate mixed-effects model for mixed-type response variables subject to item nonresponse. We apply this method to two data structures where the data are missing completely at random by design. We use empirical data from two separate studies: a survey of pet owners and a dataset from the National Resources Inventory. In these applications, our proposed method leads to improvements relative to a direct estimator and a predictor based on a univariate model.