Cross-domain recommendation (CDR) aims to leverage the correlation of users' behaviors in both the source and target domains to improve the user preference modeling in the target domain. Conventional CDR methods typically explore the dual-relations between the source and target domains' behaviors. However, this may ignore the informative mixed behaviors that naturally reflect the user's global preference. To address this issue, we present a novel framework, termed triple sequence learning for cross-domain recommendation (Tri-CDR), which jointly models the source, target, and mixed behavior sequences to highlight the global and target preference and precisely model the triple correlation in CDR. Specifically, Tri-CDR independently models the hidden representations for the triple behavior sequences and proposes a triple cross-domain attention (TCA) method to emphasize the informative knowledge related to both user's global and target-domain preference. To comprehensively explore the cross-domain correlations, we design a triple contrastive learning (TCL) strategy that simultaneously considers the coarse-grained similarities and fine-grained distinctions among the triple sequences, ensuring the alignment while preserving information diversity in multi-domain. We conduct extensive experiments and analyses on six cross-domain settings. The significant improvements of Tri-CDR with different sequential encoders verify its effectiveness and universality. The code will be released upon acceptance.