Social scientists have long documented that many components of socioeconomic status such as income and education have strong ties across generations. However, health status, arguably a more critical component of welfare, has largely been ignored. We fill this void by providing the first estimates of the Intergenerational Health Association (IHA) that are explicitly based on a non-linear latent variable model. We develop an estimation procedure for a non-linear model with categorical outcomes in which the latent index is a mixed-linear model and contains covariates that might not vary within cross-sectional units. Adjusting for only age and gender, we estimate an IHA of 0.3 indicating that about one third of a parent's health status gets transmitted to their children. Once we add additional mediators to the model, we show that education, and particularly children's education, is an important transmission channel in that it reduces the IHA by one third. Finally, we show that estimates of the IHA from non-linear models are only moderately higher than those from linear models, while rank-based mobility estimates are identical.