Reflectance confocal microscopy (RCM) provides noninvasive, cellular-resolution "optical biopsies" of human skin \emph{in vivo} by acquiring en-face images at successive depths, forming a sparse z-stack. Due to optical limitations, these stacks are anisotropic 3D volumes with lateral resolution (0.5 $μ$m) $\sim$6 times higher compared to axial resolution, which is defined by the optical sectioning (3 $μ$m), limiting the interpretation of tissue. Our goal is to provide continuous-depth visualization by interpolating intermediate sections and making the 3D volume isotropic. Such a representation permits arbitrary-direction sectioning, including histopathology-like cross-sectional examination, without requiring per-patient optimization. To that end, we introduce the first RCM-specific novel-view synthesis (NVS) approach, CD-RCM, a feedforward model that predicts realistic, unseen depths from sparsely sampled RCM stacks. Classical neural rendering methods focus on reconstruction from surface-level multi-view observations. In contrast to surface-level camera views, RCM can acquire optically sectioned en-face images of tissue beyond the surface up to 200 $μ$m. However, during visualization of the RCM stacks, observations of the shallower sections (towards the surface) obscure the deeper ones. This unique axial imaging geometry and layer-dependent anatomical organization motivated our development of a tailored architectural and training framework that explicitly accounts for RCM's depth-resolved, occlusive imaging physics. Experiments demonstrate that CD-RCM achieves high-fidelity novel-view synthesis with sub-second inference time.