Individual-level variation in susceptibility to infection and transmissibility of infection can affect population-level dynamics in epidemic outbreaks. Prior work has incorporated independent variation in susceptibility or transmissibility of individuals into epidemic compartmental models. Here, we develop and assess a mathematical framework that includes covariation in susceptibility and transmissibility. We show that uncorrelated variation in susceptibility and transmissibility leads to an effective transmissibility distribution that has a constant coefficient of variation such that the epidemic dynamics match those with variation in susceptibility alone, providing a baseline for comparison across different correlation structures. Increasing the correlation between susceptibility and transmissibility increases both the speed and strength of the outbreak - and is indicative of outbreaks which might be strongly structured by contact rate variation. In contrast, negative correlations between susceptibility and transmissibility lead to overall weaker outbreaks - with the caveat that the strength of effective transmission increases over time. In either case, correlations can shift the transmissibility distribution, thereby modifying the speed of the epidemic as the susceptible population is depleted. Overall, this work demonstrates how (often unaccounted) covariation in susceptibility and transmission can shape the course of outbreaks and final outbreak sizes.