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Seismological data plays a crucial role in timely slope failure hazard assessments. However, identifying rockfall waveforms from seismic data poses challenges due to their high variability across different events and stations. To address this, we propose RockNet, a deep-learning-based multitask model capable of detecting both rockfall and earthquake events at both the single-station and local seismic network levels. RockNet consists of two submodels: the single-station model, which computes waveform masks for earthquake and rockfall signals and performs earthquake $P$ and $S$ phase picking simultaneously on single-station seismograms, and the association model, which determines the occurrences of local seismic events by aggregating hidden feature maps from the trained single-station model across all stations. Since the rockfall data is relatively scarce and may not be sufficient to train a deep-learning model effectively, we augment the dataset with abundant nonrockfall data and add additional tasks to promote shared interpretability and robustness. RockNet is trained and tested on a local dataset collected from the Luhu tribe in Miaoli, Taiwan, achieving macro F1-scores of 0.983 and 0.990 for the single-station model and the association model, respectively. Furthermore, we evaluate RockNet on an independent dataset collected from the Super-Sauze unstable slope region in France, and it demonstrates good generalization performance in discriminating earthquake, rockfall, and noise with a macro F1-score of 0.927. This study highlights the potential of deep learning in leveraging diverse types of inputs for seismic signal detection even with limited training data.