Cortical neurons are constantly active. Even in the absence of an explicit stimulus, cortical neurons are spontaneously active and display large fluctuations of their membrane potentials. The increasing amount of intracellular recordings of spontaneous activity as well as the increasing number of theories which critically rely on a characterization of spontaneous activity calls for a proper quantification of spontaneous intracellular dynamics. Here we propose a statistical model of spontaneous activity which is very flexible and remains tractable. More specifically, we propose a doubly stochastic process where the subthreshold membrane potential follows a Gaussian process and the spike emission intensity depends nonlinearly on the membrane potential as well as the previous spiking history. We first show that the model has a rich dynamical repertoire since it can capture arbitrary subthreshold autocovariances, firing- rate adaptations as well as arbitrary shapes of the action potential. We then show that this model can be efficiently learned without overfitting. We finally show that this model can be used to characterize and therefore precisely compare a wide range of intracellular in vivo recordings from various animals and recording conditions.