Hard X-ray phase-contrast imaging characterizes the electron density distribution in an object without the need for radiation absorption. The power of phase contrast to resolve subtle changes, such as those in soft tissue structures, lies in its ability to detect minute refractive bending of X-rays. Here we report a far-field, two-arm interferometer based on the new nanometric phase gratings, which can detect X-ray refraction with subnanoradian sensitivity, and at the same time overcomes the fundamental limitation of ultra-narrow bandwidths (Δλ/λ~10⁻⁴) of the current, most sensitive methods based on crystal interferometers. On a 1.5% bandwidth synchrotron source, we demonstrate clear visualization of blood vessels in unstained mouse organs in simple projection views, with over an order-of-magnitude higher phase contrast than current near-field grating interferometers.