We introduce a method for inference on the composition of a heterogeneous population using survey data, accounting for the possibility that capture heterogeneity is related to key survey variables. To deal with nonignorable nonresponse, we combine different data sources and propose the use of Fisher’s noncentral hypergeometric model in a Bayesian framework. To illustrate the potentialities of our methodology, we present a case study aimed at estimating the distribution of occupation status of Italian graduates one year after graduating, cross-classified by gender and degree program. In our case study, we account for a potential dependence between occupation status and survey response, implying the nonignorable nonresponse. Our findings show that employed people are generally more inclined to answer the questionnaire. Neglecting the nonresponse bias in such contexts might lead to overestimating the employment rate.