relation in between a categorical dependent variable and combination of independent variables
I am not sure if I correctly understand your question, but from what I understand:
You can try to convert your continuous columns to buckets, which means effectively converting them as categorical as well and then find correlation between them.
I am looking for a technique which could help us find the relation in between a categorical dependent variable and combination of independent variables (Y ~ X1*X2+X2*X3+X3*X4), here among X1 to X4 we have few categorical columns and few continuous columns. 
I am working on a classification problem and I want to check what combination of independent columns are highly related to dependent columns.