Cross-domain recommendation (CDR) mitigates data sparsity and cold-start issues in recommendation systems. While recent CDR approaches using graph neural networks (GNNs) capture complex user-item interactions, they rely on manually designed architectures that are often suboptimal and labor-intensive. Additionally, extracting valuable behavioral information from source domains to improve target domain recommendations remains challenging. To address these challenges, we propose Behavior importance-aware Graph Neural Architecture Search (BiGNAS), a framework that jointly optimizes GNN architecture and data importance for CDR. BiGNAS introduces two key components: a Cross-Domain Customized Supernetwork and a Graph-Based Behavior Importance Perceptron. The supernetwork, as a one-shot, retrain-free module, automatically searches the optimal GNN architecture for each domain without the need for retraining. The perceptron uses auxiliary learning to dynamically assess the importance of source domain behaviors, thereby improving target domain recommendations. Extensive experiments on benchmark CDR datasets and a large-scale industry advertising dataset demonstrate that BiGNAS consistently outperforms state-of-the-art baselines. To the best of our knowledge, this is the first work to jointly optimize GNN architecture and behavior data importance for cross-domain recommendation.