Image fusion technology is widely used to fuse the complementary information between multi-source remote sensing images. Inspired by the frontier of deep learning, this paper first proposes a heterogeneous-integrated framework based on a novel deep residual cycle GAN. The proposed network consists of a forward fusion part and a backward degeneration feedback part. The forward part generates the desired fusion result from the various observations; the backward degeneration feedback part considers the imaging degradation process and regenerates the observations inversely from the fusion result. The proposed network can effectively fuse not only the homogeneous but also the heterogeneous information. In addition, for the first time, a heterogeneous-integrated fusion framework is proposed to simultaneously merge the complementary heterogeneous spatial, spectral and temporal information of multi-source heterogeneous observations. The proposed heterogeneous-integrated framework also provides a uniform mode that can complete various fusion tasks, including heterogeneous spatio-spectral fusion, spatio-temporal fusion, and heterogeneous spatio-spectral-temporal fusion. Experiments are conducted for two challenging scenarios of land cover changes and thick cloud coverage. Images from many remote sensing satellites, including MODIS, Landsat-8, Sentinel-1, and Sentinel-2, are utilized in the experiments. Both qualitative and quantitative evaluations confirm the effectiveness of the proposed method.