This paper considers the asymptotic behavior of the outage probability of two-source block-fading SISO interference channels (IFC) in the high-SNR regime. As opposed to previous works, we characterize the diversity, i.e., exponent of the outage probability, for asymmetric networks, that is to say, for arbitrary signal and interference levels at the receivers. Our result is not just a simple extension of previous results for symmetric networks, as our setting covers scenarios that are not possible in symmetric networks, such as the case of "mixed" interference, i.e., when difference sources have different distances from their intended receivers. We derive upper and lower bounds on the diversity. We show that, when the channel is symmetric and the interference is strong (above a value depending on the fading of the direct link), sending all common information is optimal, while when the interference is comparably weaker than the threshold, achievable schemes without rate splitting do not meet the diversity upper bound in general. Similar results hold in the mixed interference case.