Rather than traditional position control, impedance control is preferred to ensure the safe operation of industrial robots programmed from demonstrations. However, variable stiffness learning studies have focused on task performance rather than safety (or compliance). Thus, this paper proposes a novel stiffness learning method to satisfy both task performance and compliance requirements. The proposed method optimizes the task and compliance objectives (T/C objectives) simultaneously via multi-objective Bayesian optimization. We define the stiffness search space by segmenting a demonstration into task phases, each with constant responsible stiffness. The segmentation is performed by identifying impedance control-aware switching linear dynamics (IC-SLD) from the demonstration. We also utilize the stiffness obtained by proposed IC-SLD as priors for efficient optimization. Experiments on simulated tasks and a real robot demonstrate that IC-SLD-based segmentation and the use of priors improve the optimization efficiency compared to existing baseline methods.