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The discharge with liquid non-metallic electrodes (DLNME) was investigated. The discharge burnt steadily with a DC power supply between two streams of weakly conducting liquid (tap water) in open air at atmospheric pressure. The metallic current leads were inserted into the streams and were covered by a 5 mm thick water layer. The discharge burnt in volumetric (diffuse) form with fairly high voltage (~3 kV between leads) and low current density (~0.2-0.25 A cm-2). The plasma state in the inter-electrode gap was studied by spectroscopy, microwave sounding and electrical probe technique. The rotational and vibrational temperatures of N2 electronically excited molecules were measured. The absolute radiation values of different species were obtained as a function of position in the gap. The electric field E and the concentration of charged particles were obtained. The value of parameter E/Ng was estimated (Ng being the gas concentration). The density of water vapour in the discharge column was estimated. The results obtained show that DLNME generate molecular plasma at high pressure but out of thermal equilibrium. The properties of DLNME make it promising for various engineering applications, including those in plasma chemistry.