This article presents a probabilistic formulation for modeling earthquake rupture processes of mainshocks. A correlated multivariate Bernoulli distribution is used to model rupture occurrence. The model captures time interaction through the use of Brownian passage-time distributions to assess rupture interarrival in multiple sections of the fault, and it also considers spatial interaction through the use of spatial correlograms. The correlograms represents the effect of rupture nucleation and propagation. This model is proposed as an attractive alternative to existing probabilistic models because it (1) incorporates time and space interactions of mainshocks, (2) preserves the marginal distributions of interarrival times after including spatial rupture interactions, that is, model consistency, and (3) has an implicit physical interpretation aligned with rupture behavior observations. The proposed model is applied to assess the occurrence of large interface earthquakes in the subduction fault along the coast of Lima, Peru. The model matches well both the annual magnitude exceedance rates and the average seismic moment release in the tectonic region. The Akaike information criterion (AIC) test confirms that our model performs statistically better than models that do not capture earthquake space interactions. AIC also shows that the spherical correlogram outperforms the exponential correlogram at reproducing earthquake data. Finally, time-dependent seismic hazard in the region is calculated, and the results demonstrate that by accounting for recent earthquake occurrences, the inclusion of time-dependent effects can reduce the 30 yr seismic hazard by a factor of 4.