An important business domain that relies heavily on advanced statistical- and machine learning algorithms to support operational decision-making is customer retention management. Customer churn prediction is a crucial tool to support customer retention. It allows an early identification of customers who are at risk to abandon the company and provides the ability to gain insights into why customers are at risk. Hence, customer churn prediction models should complement predictive performance with model insights. Inspired by their ability to reconcile strong predictive performance and interpretability, this study introduces rule ensembles and their extension, spline-rule ensembles, as a promising family of classification algorithms to the customer churn prediction domain. Spline-rule ensembles combine the flexibility of a tree-based ensemble classifier with the simplicity of regression analysis. They do, however, neglect the relatedness between potentially conflicting model components which can introduce unnecessary complexity in the models and compromises model interpretability. To tackle this issue, a novel algorithmic extension, spline-rule ensembles with sparse group lasso regularization (SRE-SGL) is proposed to enhance interpretability through structured regularization. Experiments on fourteen real-world customer churn data sets in different industries (i) demonstrate the superior predictive performance of spline-rule ensembles with sparse group lasso over a set well yet powerful benchmark methods in terms of AUC and top decile lift; (ii) show that spline-rule ensembles with sparse group lasso regularization significantly outperform conventional rule ensembles whilst performing at least as well as conventional spline-rule ensembles; and (iii) illustrate the interpretable nature of a spline-rule ensemble model and the advantage of structured regularization in SRE-SGL by means of a case study on customer churn prediction for a telecommunications company.