Collaborative clinical decision support is often constrained by governance and privacy rules that prevent pooling patient-level records across institutions. We present a hybrid privacy-preserving framework that combines Federated Learning (FL) and Split Learning (SL) to support decision-oriented healthcare modeling without raw-data sharing. The approach keeps feature-extraction trunks on clients while hosting prediction heads on a coordinating server, enabling shared representation learning and exposing an explicit collaboration boundary where privacy controls can be applied. Rather than assuming distributed training is inherently private, we audit leakage empirically using membership inference on cut-layer representations and study lightweight defenses based on activation clipping and additive Gaussian noise. We evaluate across three public clinical datasets under non-IID client partitions using a unified pipeline and assess performance jointly along four deployment-relevant axes: factual predictive utility, uplift-based ranking under capacity constraints, audited privacy leakage, and communication overhead. Results show that hybrid FL-SL variants achieve competitive predictive performance and decision-facing prioritization behavior relative to standalone FL or SL, while providing a tunable privacy-utility trade-off that can reduce audited leakage without requiring raw-data sharing. Overall, the work positions hybrid FL-SL as a practical design space for privacy-preserving healthcare decision support where utility, leakage risk, and deployment cost must be balanced explicitly.