I have two variables X and Y. X is continuous, while Y is semicontinuous. Specifically, Y continuous on strictly positive values and has positive mass at 0.

What would be the optimal way to measure dependence between these two variables?

I am thinking of maybe separately measuring the dependence on the binary part of Y (correlation of X with Y_positive/Y_zero) and then, on positive Y values, measure the spearman correlation with X. But I do not know if this is a sensible approach.