We report on the fabrication and mid-infrared transmission properties of free-standing thin metal films, periodically patterned with holes at periods down to 2 microns and area of 3x3 mm2. Square grids were fabricated by electron beam lithography and deep-etching techniques and display substrateless holes, with the metal being supported by a patterned dielectric silicon nitride membrane. The mid-infrared transmission spectra of the substrateless grid display extraordinary transmission peaks and resonant absorption lines with a Q-factor up to 22. These spectral features are due to the interaction of the radiation with surface plasmon modes. The high transmittivity and the negative value of the dielectric constant at selected frequencies make our substrateless structures ideal candidates for the fabrication of mid-infrared metamaterials.