This paper proposes the hybrid framework of privacy preserving that combines the concept of federated learning and homomorphic encryption with differential privacy, to address the privacy issue of collaborative machine learning for healthcare application. The proposed approach makes three contributions: (1) multi-layered architecture using federated learning in combination homomorphic encryption (based on CKKS scheme) and differential privacy that offers defense against inference attacks at different layers, (2) the implementation which alleviates the computational overhead compared to homomorphic encryption only with optimised cryptographic parameters, and (3) the application of the Grasshopper-Black Hole Optimization (G-BHO) for the optimisation of privacy parameters (e, deltas, gradient clipping thresholds) in order to balance the privacy-utility trade-off. Cryptographic keys are produced using the principles of cryptographically secure random number generation. Experimental evaluation on two healthcare data sets (MIMIC-III and chest X rays of the patients of Covid-19) to compare the hybrid approach to the single technique baselines in four metrics: classification accuracy (93.0±1.2% vs. 89.0±1.5% for federated learning only), differential privacy guarantee (ε=0.7, δ=10⁻⁵), computational overhead (2.5x baseline vs. 8x for homomorphic encryption only) and the resistance to membership inference attacks (92% vs. 68%) The observed improvement in the accuracy is unexpected, and potentially a consequence of side-effects due to the effects of the regularization in the differential privacy noise; this finding needs to be further explored in theory. The evaluation is restricted to the tasks of healthcare classification, while generalization to other domains needs more validation. The main contribution is an empirical proof that by using a combination of several privacy mechanisms, it will be possible to achieve a stronger attack resistance with a lower computational overhead than by using homomorphic encryption alone.