We develop a flexible bivariate spatio-temporal Hawkes process model to analyze patterns of terrorism. Previous applications of point process methods to political violence data have mainly utilized temporal Hawkes process models, neglecting spatial variation in these attack patterns. This limits what can be learned from these models, as any effective counter-terrorism strategy requires knowledge on both when and where attacks are likely to occur. Even the existing work that does exist on spatio-temporal Hawkes processes impose restrictions on the triggering function that are not well-suited for terrorism data. Therefore, we generalize the structure of the spatio-temporal triggering function considerably, allowing for nonseprability, nonstatitionarity, and cross-triggering (i.e., across the groups). To demonstrate the utility of our model, we analyze two samples of real-world terrorism data: Afghanistan (2002-2013) and Nigeria (2010-2017). Jointly, these two studies demonstrate that our model dramatically outperforms standard Hawkes process models, besting widely-used alternatives in overall model fit and revealing spatio-temporal patterns that are, by construction, masked in these models (e.g., increasing dispersion in cross-triggering over time).