Neural Radiance Fields (NeRFs) have shown great potential in novel view synthesis. However, they struggle to render sharp images when the data used for training is affected by motion blur. On the other hand, event cameras excel in dynamic scenes as they measure brightness changes with microsecond resolution and are thus only marginally affected by blur. Recent methods attempt to enhance NeRF reconstructions under camera motion by fusing frames and events. However, they face challenges in recovering accurate color content or constrain the NeRF to a set of predefined camera poses, harming reconstruction quality in challenging conditions. This paper proposes a novel formulation addressing these issues by leveraging both model- and learning-based modules. We explicitly model the blur formation process, exploiting the event double integral as an additional model-based prior. Additionally, we model the event-pixel response using an end-to-end learnable response function, allowing our method to adapt to non-idealities in the real event-camera sensor. We show, on synthetic and real data, that the proposed approach outperforms existing deblur NeRFs that use only frames as well as those that combine frames and events by +6.13dB and +2.48dB, respectively.