Wireless signal recognition is becoming increasingly more significant for spectrum monitoring, spectrum management, and secure communications. Consequently, it will become a key enabler with the emerging fifth-generation (5G) and beyond 5G communications, Internet of Things networks, among others. State-of-the-art studies in wireless signal recognition have only focused on a single task which in many cases is insufficient information for a system to act on. In this work, for the first time in the wireless communication domain, we exploit the potential of deep neural networks in conjunction with multi-task learning (MTL) framework to simultaneously learn modulation and signal classification tasks. The proposed MTL architecture benefits from the mutual relation between the two tasks in improving the classification accuracy as well as the learning efficiency with a lightweight neural network model. Additionally, we consider the problem of heterogeneous wireless signals such as radar and communication signals in the electromagnetic spectrum. Accordingly, we have shown how the proposed MTL model outperforms several state-of-the-art single-task learning classifiers while maintaining a lighter architecture and performing two signal characterization tasks simultaneously. Finally, we also release the only known open heterogeneous wireless signals dataset that comprises of radar and communication signals with multiple labels.