We use nonparametric and parametric demand analysis to empirically estimate a credit card-augmented monetary asset demand system, based on the Minflex Laurent flexible functional form, and a sample period that includes the 2007–2009 global financial crisis and the COVID-19 pandemic. We also use multivariate copulae in an attempt to capture various patterns of dependence structures. In doing so, we relax the joint normality assumption of the errors of the demand system and estimate the model without having to delete one equation as is usually the practice. We show that the Minflex Laurent copula-based demand system produces a higher income elasticity for credit card transaction services and higher Morishima elasticities between credit card transaction services and monetary assets compared to the traditional estimation of the Minflex Laurent demand system. We also show that credit cards are substitutes for monetary assets and that there is lower tail dependence between the demand for credit card transaction services and transaction balances.