We report a three-phase slug flow and parallel-slug flow as two major flow patterns found under the nitrogen-decane-water flow through a glass microfluidic chip which features a long microchannel with a hydraulic diameter of 98 µm connected to a cross-flow mixer. The three-phase slug flow pattern is characterized by a flow of decane droplets containing single elongated nitrogen bubbles, which are separated by water slugs. This flow pattern was observed at a superficial velocity of decane (in the range from about 0.6 to 10 mm/s) typically lower than that of water for a given superficial gas velocity in the range of 30 to 91 mm/s. The parallel-slug flow pattern is characterized by a continuous water flow in one part of the channel cross section and a parallel flow of decane with dispersed nitrogen bubbles in the adjacent part of the channel cross section, which was observed at a superficial velocity of decane (in the range from about 2.5 to 40 mm/s) typically higher than that of water for each given superficial gas velocity. Three-phase slug flow can be seen as a superimposition of both decane-water and nitrogen-decane slug flows observed in the chip when the flow of the third phase (viz. nitrogen or water, respectively) was set at zero. Parallel-slug flow can be seen as a superimposition of the decane-water parallel flow and the nitrogen-decane slug flow observed in the chip under the corresponding two-phase flow conditions. In case of small capillary numbers (Ca « 0.1) and Weber numbers (We « 1), the developed two-phase pressure drop model under slug flow has been extended to obtain a three-phase slug flow model in which the ‘nitrogen-in-decane’ droplet is assumed as a pseudo-homogeneous droplet with an effective viscosity. The parallel flow and slug flow pressure drop models have been combined to obtain a parallel-slug flow model. The obtained models describe the experimental pressure drop with a standard deviation of 8% and 12% for three-phase slug flow and parallel-slug flow, respectively. An example is given to illustrate the model uses in designing bifurcated microchannels that split three-phase slug flow for high-throughput processing.