The goal of this research is to study physicians' prescription decisions and patients' drug request behaviors jointly. We have developed a new zero-inflated multinomial (ZiMNL) choice model to study patient drug request data with excessive zero requests and a standard multinomial logit (MNL) model to capture physician prescriptions decisions. The two models are joined by a flexible nonparametric multivariate distribution for their random effects. We also adopt an analytically consistent expression for the interaction effect in our non-linear and joint modeling framework. We apply our model to a unique physician panel data set from the Erectile Dysfunction category. Our key empirical findings include the following: (1) the triggering of drug requests by DTCA is complicated with category level DTCA reducing patients' probability of making drug requests and drug specific DTCA driving drug requests for the advertised drug; (2) patient characteristics may play a role in the impact of DTCA on drug requests and the impact of patient requests on physicians' prescription decisions; (3) patient drug requests have a significant impact on physicians' prescription decisions and patients can be consistent with physicians in choosing a drug based on patient diagnosis level and some unobserved factors; (4) there are significant correlations among physician-level random effects that drive both patients' drug requests and physicians' prescription decisions, which validates the joint modeling approach.