A new interpretation of the discontinuity factor (DF) for scalar flux, partial current, and angular flux is discussed. Conventionally, the DF is considered as the discontinuous condition of scalar flux, partial current, or angular flux at an interface. In the new interpretation, the DF is considered as the refractive index of materials for partial current or angular flux that conserves odd-parity or odd-moment angular flux at an interface of different materials. It is related to the transmission and reflection of partial current or angular flux at an interface where different materials are adjacent. Using the present interpretation, a fundamental issue of neutron balance (i.e., artificial loss or production of neutrons at an interface due to discontinuous condition), which would appear in the conventional interpretation of DF, can be resolved.