Interpersonal sensorimotor synchronization (interpersonal SMS) is the foundation of complex human social interaction. Previous studies primarily focused on the individual cognitive processes of interpersonal SMS. However, all individuals compose an entire interaction system with emerged holistic properties during interpersonal SMS. Therefore, we proposed the `holistic cognitive and neural processes' of interpersonal SMS and defined quantitative measurements that included Holistic Correction Gain (HCG), Holistic Timekeeper Variance (HTV) and Holistic Motor Variance (HMV) based on linear error correction model and inter-brain couplings obtained by hyperscanning technique. We performed a joint-tapping experiment including bidirectional and unidirectional conditions using functional near-infrared spectroscopy (fNIRS) hyperscanning to evaluate effects of these holistic processes on synchronization performance. We found that the dyads' performance highly correlated with the integrated effect of holistic cognitive processes in both conditions. Each holistic cognitive process played different roles in interpersonal SMS. HCG was critical to maintain synchronization. HTV related to mentalizing others' behavior. Holistic neural process, the inter-brain coupling of right prefrontal cortex (PFC), was significantly different between bidirectional and unidirectional conditions, which suggested the existence of neural markers at holistic level in interpersonal SMS.