The generalized propensity score (GPS) is an extension of the propensity score for use withquantitative or continuous exposures (e.g., dose of medication or years of education). Current GPS methods allow estimation of the dose-response relationship between a single continuous exposure and an outcome. However, in many real-world settings, there are multiple exposures occurring simultaneously that could be causally related to the outcome. We propose a multivariate GPS method (mvGPS) that allows estimation of a dose-response surface that relates the joint distribution of multiple continuous exposure variables to an outcome. The method involves generating weights under a multivariate normality assumption on the exposure variables. Focusing on scenarios with two exposure variables, we show via simulation that the mvGPS method can achieve balance across sets of confounders that may dier for dierent exposure variables and reduces bias of the treatment-eect estimates under a variety of data generating scenarios. We apply the mvGPS method to an analysis of the joint eect of two types of intervention strategies to reduce childhood obesity rates. The methods can be implemented using the mvGPS R package available on CRAN.