We present a detailed study of the neutral and ionized gas phases in the galactic wind for the nearby starburst galaxy NGC 5394 based on new integral field spectroscopy obtained with the INTEGRAL fibre system at the William Herschel Telescope. The neutral gas phase in the wind is detected via the interstellar Na I D doublet absorption. After a careful removal of the stellar contribution to these lines, a significant amount of neutral gas (˜107 M⊙) is detected in a central region of ˜1.75 kpc size. This neutral gas is blueshifted by ˜165 km s-1 with respect to the underlying galaxy. The mass outflow of neutral gas is comparable to the star formation rate of the host galaxy. Simultaneously, several emission lines (Hα, [N II], [S II]) are also analysed looking for the ionized warm phase counterpart of the wind. A careful kinematic decomposition of the line profiles reveals the presence of a secondary, broader, kinematic component. This component is found roughly in the same region where the Na I D absorption is detected. It presents higher [N II]/Hα and [S II]/Hα line ratios than the narrow component at the same locations, indicative of contamination by shock ionization. This secondary component also presents blueshifted velocities, although smaller than those measured for the neutral gas, averaging to ˜-30 km s-1. The mass and mass outflow rate of the wind is dominated by the neutral gas, of which a small fraction might be able to escape the gravitational potential of the host galaxy. The observations in this system can be readily understood within a bipolar gas flow scenario.