The collection of pathogen samples and subsequent genetic sequencing enables the reconstruction of phylogenies, shedding light on transmission dynamics. However, many existing phylogenetic methods fall short by neglecting within-host diversity and the impact of transmission bottlenecks, leading to inaccuracies in understanding epidemic spread. This paper introduces the Transmission Tree (TnT) model, which leverages multiple pathogen gene trees to more accurately model transmission history. By extending the Bayesian phylogenetic analysis software BEAST2, TnT integrates the sampled ancestor birth-death model for transmission trees and the multi-species coalescent model for pathogen gene trees. This integration allows for the consideration of critical factors like transmission orientation, incomplete lineage sorting, and within- and between-host diversity. Notably, TnT incorporates an analytical approach to address unobserved transmission events, crucial in scenarios with incomplete sampling. Through theoretical evaluation and application to a real-world HIV transmission chain, we demonstrate that TnT offers a robust solution to improve understanding of epidemic dynamics by effectively combining pathogen gene sequences and clinical data.