Three-dimensional structure of the Aquila Rift of magnetized neutral gas is investigated by analysing H I and CO line data. The projected distance on the Galactic plane of the H I arch of the Aquila Rift is r(perpendicular to) similar to 250 pc from the Sun. The H I arch emerges at l similar to 30 degrees, reaches to altitudes as high as similar to 500 pc above the plane at l similar to 350 degrees, and returns to the disc at l similar to 270 degrees. The extent of arch at positive latitudes is similar to 1 kpc and the width is similar to 100 pc. The eastern root is associated with the giant molecular cloud complex, which is the main body of the optically defined Aquila Rift. The H I and molecular masses of the Rift are estimated to be M-HI similar to 1.4 x 10(5)M circle dot and M-H2 similar to 3 x 10(5)M circle dot. Gravitational energies to lift the gases to their heights are E-grav:H I similar to 1.4 x 10(51) erg and E-grav:H2 similar to 0.3 x 10(51) erg, respectively. Magnetic field is aligned along the HI arch of the Rift, and the strength is measured to be B similar to 10 mu Gusing Faraday rotation measures of extragalactic radio sources. The magnetic energy is estimated to be E-mag similar to 1.2 x 10(51) erg. A possible mechanism of formation of the Aquila Rift is proposed in terms of interstellar magnetic inflation by a sinusoidal Parker instability of wavelength of similar to 2.5 kpc and amplitude similar to 500 pc.