The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs. We provide several infinite families of forbidden induced subgraphs of mixed unit interval bigraphs. We also pose a conjecture concerning characterization of mixed unit interval bigraphs and verify parts of it. © Springer International Publishing AG 2018.