Integrated-magnetic interleaved boost converters are under development for high-current, high-power applications ranging from automotive to distributed generation. The operating modes of these integrated-magnetic converters are complex and are also a function of the conduction of the lower inverse diode. A reverse-blocking diode or RB IGBT may be preferred for the lower switch, which introduces additional modes. This paper presents an investigation of the various discontinuous-current (DCM) modes of operation of the integrated-magnetic interleaved two-phase boost converter. The various DCM modes of the converter are identified together with their sub-modes of operation. The steady-state operating characteristics and waveforms for the many DCM modes will be presented for the converter family. Mode maps will be developed to map the converter operation across the modes over the operating range. Experimental validation is presented from a 3.6 kW laboratory prototype.