One of the most recent additions to the family of two-dimensional (2D) materials, graphitic C3N3 (g-C3N3), has been considered a viable contender for biomedical applications, although its potential toxicity remains elusive. We perform all-atom molecular dynamics simulations to decipher the interactions between model lipid membranes and g-C3N3 as a first step toward exploring the cytotoxicity induced at the nanoscale. We show that g-C3N3 can easily insert into the cellular membranes following a multistage mechanism consisting of simultaneous desolvation of the 2D material along with enrichment of nanomaterial-lipid interactions. Free energy calculations indicate that g-C3N3 is more stable in a membrane-bound state compared to an aqueous solution; however, the insertion of the material does not disturb the structural integrity of lipid membranes. After being inserted into a membrane, g-C3N3 is unlikely to be released into the cellular environment and is incapable of extracting lipid molecules from the membrane. The nature of interaction between the 2D material and membranes is found to be independent of the nanomaterial size. Also, the performance of g-C3N3 toward biomolecular delivery is shown to be significantly improved compared to the state-of-the-art 2D materials graphene and hexagonal boron nitride (h-BN). It is revealed that, the affinity of g-C3N3 toward lipid membranes is weaker compared to the nanotoxic graphene and h-BN, while being marginally higher than h2D-C2N, which in turn, increases the biocompatibility of the material, thereby brightening its future as a noncytotoxic material for forthcoming biomedical applications.