Malware open-set recognition (MOSR) aims at jointly classifying malware samples from known families and detect the ones from novel unknown families, respectively. Existing works mostly rely on a well-trained classifier considering the predicted probabilities of each known family with a threshold-based detection to achieve the MOSR. However, our observation reveals that the feature distributions of malware samples are extremely similar to each other even between known and unknown families. Thus the obtained classifier may produce overly high probabilities of testing unknown samples toward known families and degrade the model performance. In this paper, we propose the Multi-modal Dual-Embedding Networks, dubbed MDENet, to take advantage of comprehensive malware features (i.e., malware images and malware sentences) from different modalities to enhance the diversity of malware feature space, which is more representative and discriminative for down-stream recognition. Last, to further guarantee the open-set recognition, we dually embed the fused multi-modal representation into one primary space and an associated sub-space, i.e., discriminative and exclusive spaces, with contrastive sampling and rho-bounded enclosing sphere regularizations, which resort to classification and detection, respectively. Moreover, we also enrich our previously proposed large-scaled malware dataset MAL-100 with multi-modal characteristics and contribute an improved version dubbed MAL-100+. Experimental results on the widely used malware dataset Mailing and the proposed MAL-100+ demonstrate the effectiveness of our method.