Bipartite networks can represent various kinds of structures, dynamics, and interaction patterns found in social activities. M. E. J. Newman proposed a measure by which you can quantitatively evaluate the quality of network division, but his work is only applicable to uniform networks. This article extends his work and proposes a new modularity measure that can be applied to bipartite networks as well. Unlike the bipartite modularity measures previously proposed, the new measure acknowledges the fact that each individual in the society has more than just one aspect, and can thus be used to extract multi-faceted community structures from bipartite networks. The mathematical properties of the proposal is examined and compared with previous work. Empirical evaluation is conducted by using a data set synthesized from an artificial model and a real-life data set found in the field of ethnography.