The 3GPP standardization rapidly moves forward with studies of a wide-bandwidth waveform as well as an adaptation of the emerging 5G new radio (NR)-based access to the unlicensed spectrum (NR-U). One of the basic architectures for NR-U involves carrier aggregation of an anchor-licensed-NR carrier and a secondary carrier in unlicensed spectrum, which altogether allows for seamless traffic offloading in scenarios where multi-gigabit data rates are required. While today's research on NR-U addresses mostly physical-and protocol-layer aspects, a system-level performance of the NR-U offloading mechanisms has not been investigated thoroughly. In this paper, we develop a mathematical queuing-theoretic framework that is mindful of the specifics of millimeter-wave (mmWave) session dynamics and may serve as a flexible tool for the analysis of various strategies for the integrated use of licensed and unlicensed mmWave bands in terms of the session drop probability and system utilization. To illustrate this, we select three distinct strategies (based on sequential service, probabilistic offloading, or proportional splitting), and complement our mathematical models with a detailed performance evaluation in a representative massive augmented/virtual reality scenario. Based on this quantitative analysis of the selected schemes, we conclude that proportional splitting of traffic between the two mmWave bands leads to a better performance. We believe that the contributed mathematical analysis can become an important building block in further system development and service optimization across many usage scenarios.