We present PhoMoH, a neural network methodology to construct generative models of photorealistic 3D geometry and appearance of human heads including hair, beards, clothing and accessories. In contrast to prior work, PhoMoH models the human head using neural fields, thus supporting complex topology. Instead of learning a head model from scratch, we propose to augment an existing expressive head model with new features. Concretely, we learn a highly detailed geometry network layered on top of a mid-resolution head model together with a detailed, local geometry-aware, and disentangled color field. Our proposed architecture allows us to learn photorealistic human head models from relatively little data. The learned generative geometry and appearance networks can be sampled individually and allow the creation of diverse and realistic human heads. Extensive experiments validate our method qualitatively and across different metrics.