# Formula for copulas of bivariate mixed (discrete and continuous) data

I have a question as I am new to copulas. I have bivariate data (X,Y), one is discrete and one is continuous distributed. Can I use the usual formula for the common density function given by $$f_X(x) \cdot f_Y(y) \cdot \frac{\partial^2 C(u,v,\alpha)}{\partial u \partial v}$$ where $u=F_X$, $v=F_y$ and C is a (archimedean) Copula, or does this only hold for two continuous random variables? Thanks!