The low-lying Netherlands is at risk from multiple threats of sea level rise, storm surges and extreme river discharges. Should these occur simultaneously, a catastrophe will be at hand. Knowledge about the likelihood of simultaneous occurrence or the so-called "compound effect" of such threats is essential to provide guidance on legislation for dike heights, flood barrier design and water management in general. In this study, we explore the simultaneous threats of North Sea storm surges and extreme Rhine river discharge for the current and future climate in a large 17-member global climate model ensemble. We use a simple approach, taking proxies of north-northwesterly winds over the North Sea and multiple~day precipitation averaged over the Rhine basin for storm surge and discharge respectively, so that a sensitivity analysis is straightforward to apply. By investigating soft extremes, we circumvent the need to extrapolate the data and thereby permit the model's synoptic development of the extreme events to be inspected. Our principle finding based on the climate model data is that, for the current climate, the probability of extreme surge conditions following extreme 20-day precipitation sums is around 3 times higher than that estimated from treating extreme surge and discharge probabilities as independent, as previously assumed. For the future climate (2070–2100), the assumption of independence cannot be rejected, at least not for precipitation sums exceeding 7 days.