Asthma is an inflammatory airway disease that affects 22 million Americans in the United States. Research has found associations between impaired respiratory function, including asthma and increased symptoms among asthmatics, and common indoor air pollutants, including tobacco smoke exposure and volatile organic compounds (VOCs). However, findings linking VOC exposure and asthma are inconsistent and studies are of mixed quality due to design limitations, challenges measuring VOC exposure, small sample sizes, and suboptimal statistical methodologies. Because of the correlation between tobacco smoke exposure and VOCs, and associations between both tobacco smoke and VOCs with respiratory function, it is crucial that statistical methodology employed to assess links between respiratory function and individual air pollutants control for these complex relationships. This research uses Structural Equation Modeling (SEM) to assess the relationships between respiratory function, tobacco smoke exposure, and VOC exposure among a nationally-representative sample of adolescents. SEM allows for multiple outcome variables, the inclusion of both observed and latent variables, and controls the effects of confounding and correlated variables, which is critically important and is lacking in earlier studies when estimating the effects of correlated air pollutants on respiratory function. We find evidence of associations between respiratory function and some types of VOCs, even when controlling for the effects of tobacco smoke exposure and additional covariates. Furthermore, we find that poverty has an indirect effect on respiratory function through its relationships with tobacco smoke exposure and some types of VOCs. This analysis demonstrates how SEM is a robust analytic tool for assessing associations between respiratory function and multiple exposures to pollutants.