Opioid misuse is a significant public health issue and a national epidemic with a high prevalence of associated morbidity and mortality. The epidemic is particularly severe in Ohio which has some of the highest overdose rates in the country. It is important to understand spatial and temporal trends of the opioid epidemic to learn more about areas that are most affected and to inform potential community interventions and resource allocation. We propose a multivariate spatio-temporal model to leverage existing surveillance measures, opioid-associated deaths and treatment admissions, to learn about the underlying epidemic for counties in Ohio. We do this using a temporally varying spatial factor that synthesizes information from both counts to estimate common underlying risk which we interpret as the burden of the epidemic. We demonstrate the use of this model with county-level data from 2007-2018 in Ohio. Through our model estimates, we identify counties with above and below average burden and examine how those regions have shifted over time given overall statewide trends. Specifically, we highlight the sustained above average burden of the opioid epidemic on southern Ohio throughout the 12 years examined.