A novel multiplexing scheme for integrated networks characterized by the coexistence of circuitswitched and packet‐switched traffic is described in this paper. The new scheme is realized by a reinforcement of the basic movable boundary hybrid‐switching technique, by incorporating an adaptive interpolation within the circuit‐switched subsystem. The adaptation mechanism is controlled by the level of congestion in the packet queue. A precise queueing model for the multiplexer is developed and an analytical evaluation of the key performance parameters of interest, namely the loss probability and expected delay of the packet‐switched subsystem, and the freeze‐out fraction of the circuit‐switched subsystem, is conducted. The results of several numerical studies are presented to describe the performance of the multiplexer under different conditions. Of particular significance resulting from these studies is the trade‐off between the freeze‐out fraction of the circuit‐switched subsystem and the loss probability of the packet‐switched subsystem; this trade‐off may be exploited in a systematic design of the interrated multiplexer tailored to specific applications.