Bayesian Networks (BNs) are widely utilized across various industrial sectors to optimize processes, with an emerging focus on the collaboration across multiple parties. While most realistic scenarios require handling a mixture of categorical and continuous data simultaneously, the current state-of-the-art only supports collaborative inference on purely discrete models. The Junction Tree enables efficient and accurate inference on hybrid models but has not been implemented for confidential scenarios yet. To address this gap, we introduce Hybrid CCJT, an innovative framework for confidential multiparty inference in hybrid domains, offering: (i) a method to construct a collaborative, strongly-rooted junction tree for efficient and secure inference, (ii) a confidential-
preserving inference protocol for Hybrid BNs, (iii) an optimized message-passing scheme that
improves communication efficiency even in the purely discrete domain. Our extensive evaluation
show that Hybrid CCJT improves the predictive accuracy of continuous target variables by an average of 32% in Mean Squared Error and reduce the communication cost up to 86-fold, against the best state-of-the-art baseline.