Successful bone regeneration benefits from three-dimensional (3D) bioresorbable scaffolds that mimic the hierarchical architecture and mechanical characteristics of native tissue extracellular matrix (ECM). A scaffold platform that integrates unique material chemistry with nanotopography while mimicking the 3D hierarchical bone architecture and bone mechanics is reported. A biocompatible dipeptide polyphosphazene-polyester blend is electrospun to produce fibers in the diameter range of 50–500 nm to emulate dimensions of collagen fibrils present in the natural bone ECM. Various electrospinning and process parameters are optimized to produce blend nanofibers with good uniformity, appropriate mechanical strength, and suitable porosity. Biomimetic 3D scaffolds are created by orienting blend nanofiber matrices in a concentric manner with an open central cavity to replicate bone marrow cavity, as well as the lamellar structure of bone. This biomimicry results in scaffold stress–strain curve similar to that of native bone with a compressive modulus in the mid-range of values for human trabecular bone. Blend nanofiber matrices support adhesion and proliferation of osteoblasts and show an elevated phenotype expression compared to polyester nanofibers. Furthermore, the 3D structure encourages osteoblast infiltration and ECM secretion, bridging the gaps of scaffold concentric walls during in vitro culture. The results also highlight the importance of in situ ECM secretion by cells in maintaining scaffold mechanical properties following scaffold degradation with time. This study for the first time demonstrates the feasibility of developing a mechanically competent nanofiber matrix via a biomimetic strategy and the advantages of polyphosphazene blends in promoting osteoblast phenotype progression for bone regeneration.