In customer service (CS), customers pose questions that will be answered by customer service staff, and the communication in CS is a typical multi-round conversation. However, there are no explicit correspondences among conversational utterances, and obtaining the explicit alignments of those utterances not only contributes to dialogue analysis but also provides valuable data for learning intelligent dialogue systems. In this paper, we first present a study on utterance alignment (UA) in CS. We divide the alignment of utterances into four types: None, One-to-One, One-to-Many and Jump. The direct design models such as rule-based and matching-based methods are often only good at solving part of types, and the major reason is that they ignore the interactions of different utterances. Therefore, to model the mutual influence of different utterances as well as their alignments, we propose a joint model which models the UA as a task of joint disambiguation and resolved by integer programming. We conduct experiments on a dataset of an in-house online CS. And the results indicate that it performs better than baseline models, especially for One-to-Many and Jump alignments.