But so what you describe sounds as if it were equivalent to using d1 and d2 separately, right?
So what you are doing mathematically is to define a distribution on the product space of the domains of the two distributions. (So e.g. sample would sample from d1 and d2 and return the concatenated vector. log_prob would split the vector, take the log_prob of d1 and d2 and return the sum.)
Best regards
Thomas