This paper considers the asymptotic behavior of two-source block-fading single-antenna Gaussian interference channels in the high-SNR regime by means of the diversity-multiplexing tradeoff (DMT). We consider a general setting where the users and the average channel gains are not restricted to be symmetric. Our results are not just extensions of previous results for symmetric networks, as our setting covers scenarios that are not possible under the symmetric assumption, such as the case of "mixed" interference, i.e., when different sources have different distances from their intended receivers. We derive lower bounds on the DMT by considering rate splitting. We show by numerical evaluations, that rate splitting improves the inner bound with respect to the previous results and coincides with the outer bound for a fairly large set of channel parameters.