<p>Partly interval-censored data with a cure fraction are commonly encountered in epidemiological and biomedical studies, where exact failure times are observed for some subjects while others fall within certain intervals. For cure survival data, two-component mixture cure models that directly model the probability of being uncured and the conditional survival function of susceptible subjects, have attracted considerable attention. However, conventional cure models typically assume linear covariate effects in both components, which may limit their flexibility and applicability for potential nonlinear relationships. In this paper, we propose a flexible semiparametric mixture cure model that incorporates parametric and nonparametric covariate structures for both the cure probability and the event-time distribution of susceptible subjects. We utilize spline-based techniques to approximate unspecified functions and implement a four-stage data augmentation approach to address the complexities inherent in the model and data structure. A computationally convenient Bayesian approach is developed to obtain posterior estimates of the model parameters. The finite-sample performance of the proposed method is evaluated through simulation studies. The practical utility of the approach is demonstrated by an analysis of child mortality data.</p>