Integrated information is a quantitative measure from information theory of how tightly all parts of a system are interconnected in terms of information exchange. In this study we show that astrocytes, playing an important role in regulation of information transmission between neurons, may contribute to a generation of positive integrated information in neuronal ensembles. Analytically and numerically we show that the presence of astrocytic regulation of neurotransmission may be essential for this information attribute in neuroastrocytic ensembles. Moreover, the proposed "spiking-bursting" mechanism of generating positive integrated information is shown to be generic and not limited to neuron-astrocyte networks and is given a complete analytic description.