Cross-domain recommendation (CDR) aims to leverage the users' behaviors in both source and target domains to improve the target domain's performance. Conventional CDR methods typically explore the dual relations between the source and target domains' behavior sequences. However, they ignore modeling the third sequence of mixed behaviors that naturally reflects the user's global preference. To address this issue, we present a novel and model-agnostic Triple sequence learning for cross-domain recommendation (Tri-CDR) framework to jointly model the source, target, and mixed behavior sequences in CDR. Specifically, Tri-CDR independently models the hidden user representations for the source, target, and mixed behavior sequences, and proposes a triple cross-domain attention (TCA) to emphasize the informative knowledge related to both user's target-domain preference and global interests in three sequences. To comprehensively learn the triple correlations, we design a novel triple contrastive learning (TCL) that jointly considers coarse-grained similarities and fine-grained distinctions among three sequences, ensuring the alignment while preserving the information diversity in multi-domain. We conduct extensive experiments and analyses on two real-world datasets with four domains. The significant improvements of Tri-CDR with different sequential encoders on all datasets verify the effectiveness and universality. The source code will be released in the future.