A model to describe internal field emission through the interface between highly n-doped Si and nitrogen (N)-doped diamond is presented. We describe the roughness on the Si surface as a collection of sharp, spherically pointed Si asperities embedded in the diamond film. These "tips" provide enhancement of the applied electric held, which, in conjunction with the high N doping of diamond, results in the formation of a Schottky barrier which allows for tunneling or internal field emission from the Si into the conduction band of diamond. This enhanced electric held is also sufficient to induce valence band tunneling from the Si into the diamond conduction band. In our model limitations on the held mediated transport of holes from the n-doped Si/diamond interface to the cathode base leads to charging of the Si asperities. This charge accumulation results in band bending in Si and a significant reduction in the valence band current. The calculated J-V characteristics for the internal field emission lead to nonlinear behavior when plotted in Fowler-Nordheim coordinates. This is a consequence of the Limitation of the conduction band current due to density of states effects at high fields in addition to the suppression of the valence band current. The calculated results are in qualitative agreement with recent field emission studies of Okano et al. [K. Okano, S. Koizumi, S. Ravi, P. Silva, and G. A. J. Amaratunga, Nature 381, 140 (1996)] for a composite n-Si and N-diamond cold cathode source. A plausible geometric argument suggests that there is also reasonable quantitative agreement.