The accurate identification of anticancer peptides (ACPs) and antimicrobial peptides (AMPs) remains a computational challenge. We propose a tri-fusion neural network termed TriNet for the accurate prediction of both ACPs and AMPs. The framework first defines three kinds of features to capture the peptide information contained in serial fingerprints, sequence evolutions, and physicochemical properties, which are then fed into three parallel modules: a convolutional neural network module enhanced by channel attention, a bidirectional long short-term memory module, and an encoder module for training and final classification. To achieve a better training effect, TriNet is trained via a training approach using iterative interactions between the samples in the training and validation datasets. TriNet is tested on multiple challenging ACP and AMP datasets and exhibits significant improvements over various state-of-the-art methods.