A suitable set of test instances, also known as benchmark problems, is a key ingredient to systematically evaluate numerical solution algorithms for a given class of optimization problems. While in recent years several solution algorithms for the class of multiobjective mixed-integer nonlinear optimization problems have been proposed, there is a lack of a well-established set of test instances to compare the performance of these algorithms and evaluate their strengths and weaknesses. Hence, in this manuscript we collect and classify test instances that have been presented in the literature so far to obtain a first collection of benchmark problems. In particular, for the classification we give an overview of important properties that potentially influence the performance of solution algorithms for multiobjective mixed-integer optimization problems and investigate these properties for previously presented test instances. Our results form a foundation for the systematic evaluation of solution algorithms as well as the development and classification of corresponding test instances in the future.