Gene dependency networks often undergo changes with respect to different disease states. Understanding how these networks rewire between two different disease states is an important task in genomic research. Although many computational methods have been proposed to undertake this task via differential network analysis, most of them are designed for a predefined data type. With the development of the high throughput technologies, gene activity measurements can be collected from different aspects (e.g., mRNA expression and DNA mutation). These different data types might share some common characteristics and include certain unique properties of data type. New methods are needed to explore the similarity and difference between differential networks estimated from different data types. In this study, we develop a new differential network inference model which identifies gene network rewiring by combining gene expression and gene mutation data. Similarities and differences between different data types are learned via a group bridge penalty function. Simulation studies have demonstrated that our method consistently outperforms the competing methods. We also apply our method to identify gene network rewiring associated with ovarian cancer platinum resistance from The Cancer Genome Atlas data. There are certain differential edges common to both data types and some differential edges unique to individual data types. Hub genes in the differential networks inferred by our method play important roles in ovarian cancer drug resistance.