We report nano field-effect transistor (nanoFET) biosensors built from the monolithic integration of graphene and graphite. The monolithic integration enables nanoscopic field-effect detection of chemical and biological signals with mechanically flexible and robust interface with biological systems in several respects. Our nanoFET biosensors exhibit superior detection sensitivity, mechanical flexibility and nanoscopic detection resolution. First, we demonstrate that electrical detection can be achieved from nanoscale electric field modulation of the graphene channel while the signal integrity is not perturbed by mechanical deflection of graphene nanoFET sensors. Such capability is introduced by the advanced design of monolithic graphene-graphite without any need for metal-graphene heterointerfaces. Second, we explore the chemical detection capability of graphene nanoFET sensors, and show that our sensors are responsive to localized chemical environmental changes/perturbations. Our nanoFET sensors not only show clear response to nanoscopic charge perturbation but also demonstrate potential 3-D sensing capability due to the advanced monolithic graphene-graphite mechanical design. These unique capabilities of our monolithic graphene-graphite bioelectronics could be exploited in chemical and biological detection and conformal interface with biological systems in the future.