Diagnostic grading of prostate cancer (PCa) relies on the examination of 2D histology sections. However, the limited sampling of specimens afforded by 2D histopathology, and ambiguities when viewing 2D cross-sections, can lead to suboptimal treatment decisions. Recent studies have shown that 3D histomorphometric analysis of glands and nuclei can improve PCa risk assessment compared to analogous 2D features. Here, we expand on these efforts by developing an analytical pipeline to extract 3D features related to perineural invasion (PNI) and lymphovascular invasion (LVI), which correlate with poor prognosis for a variety of cancers. A 3D segmentation model (nnU-Net) was trained to segment nerves and vessels in 3D datasets of archived prostatectomy specimens that were optically cleared, labeled with a fluorescent analog of H&E, and imaged with open-top light-sheet (OTLS) microscopy. PNI- and LVI-related features, including metrics describing cancer-nerve and cancer-vessel proximity, were then extracted based on the 3D nerve/vessel segmentation masks in conjunction with 3D masks of cancer-enriched regions. As a preliminary exploration of the prognostic value of these features, we trained a supervised machine learning classifier to predict 5-year biochemical recurrence (BCR) outcomes, finding that 3D PNI-related features are moderately prognostic and outperform 2D PNI-related features (AUC = 0.71 vs. 0.52). Source code is available at https://github.com/sarahrahsl/SegCIA.git.