A method for producing and separating ethanol from biomass, the method comprising the steps of: (a) introducing a liquid medium comprising biomass and a fermentation microorganism to a reactor vessel to at least partially convert the biomass in the liquid medium to ethanol; (b) effectuating a sufficient flow of the liquid medium from the reactor vessel through a first cross-flow filtration cassette to separate a permeate comprising ethanol from a retentate comprising the biomass and the fermentation microorganism; (c) directing (i) the permeate to a permeate vessel, (ii) a first portion of the retentate to the reactor vessel, and (iii) a remaining portion of the retentate to a second cross-flow filtration cassette to separate the biomass from the fermentation microorganisms, wherein the biomass is selected from the group consisting of lactose, whey, whey permeate, corn, grasses, wheat, rye, rice, potatoes, artichokes, sugar beets, sugar cane, fruits, wood by-products, wood fiber, plant fiber, paper and grasses, and wherein the cross-flow filtration cassettes comprise: an array of sheet members of generally rectangular and generally planar shape with main top and bottom surfaces, wherein the sheet members include in sequence in said array a first retentate sheet, a first filter sheet, a permeate sheet, a second filter sheet, and a second retentate sheet, wherein the liquid medium to be filtered flows across the filter sheets, solids or high-molecular-weight species of diameter larger than the filter sheet's pore size, are retained in the retentate flow, and at least a portion of the liquid medium with any permeate species diffuse through the filter sheets and enter the permeate sheet and permeate flow; wherein each of the filter and permeate sheet members in said array has at least one inlet basin opening at one end thereof, and at least one outlet basin opening at an opposite end thereof, with permeate passage openings at longitudinal side margin portions of the sheet members, wherein each of the first and second retentate sheets having a multiplicity of channel openings therein, extending longitudinally between the inlet and outlet basin openings of the sheets in the array, and being bonded to an adjacent filter sheet about peripheral end and side portions thereof, with their basin openings and permeate passage openings in register with one another and the permeate passage openings of each of the retentate sheets being circumscribingly bonded to the adjacent filter sheet, and with a central portion of each of the retentate sheets and adjacent filter sheets being unbonded to permit permeate contacting the retentate sheet to flow through the filter sheet to the permeate sheet, and wherein when the biomass is cellulosic biomass comprising one of wood by-products, wood fiber, plant fiber, paper and grasses, step (a) is a two-step process comprising converting the cellulosic biomass into sugar and then fermenting the sugar into ethanol. (a) introducing a liquid medium comprising biomass and a fermentation microorganism to a reactor vessel to at least partially convert the biomass in the liquid medium to ethanol; (b) effectuating a sufficient flow of the liquid medium from the reactor vessel through a first cross-flow filtration cassette to separate a permeate comprising ethanol from a retentate comprising the biomass and the fermentation microorganism; (c) directing (i) the permeate to a permeate vessel, (ii) a first portion of the retentate to the reactor vessel, and (iii) a remaining portion of the retentate to a second cross-flow filtration cassette to separate the biomass from the fermentation microorganisms, an array of sheet members of generally rectangular and generally planar shape with main top and bottom surfaces, wherein the sheet members include in sequence in said array a first retentate sheet, a first filter sheet, a permeate sheet, a second filter sheet, and a second retentate sheet, wherein the liquid medium to be filtered flows across the filter sheets, solids or high-molecular-weight species of diameter larger than the filter sheet's pore size, are retained in the retentate flow, and at least a portion of the liquid medium with any permeate species diffuse through the filter sheets and enter the permeate sheet and permeate flow; wherein each of the filter and permeate sheet members in said array has at least one inlet basin opening at one end thereof, and at least one outlet basin opening at an opposite end thereof, with permeate passage openings at longitudinal side margin portions of the sheet members, wherein each of the first and second retentate sheets having a multiplicity of channel openings therein, extending longitudinally between the inlet and outlet basin openings of the sheets in the array, and being bonded to an adjacent filter sheet about peripheral end and side portions thereof, with their basin openings and permeate passage openings in register with one another and the permeate passage openings of each of the retentate sheets being circumscribingly bonded to the adjacent filter sheet, and with a central portion of each of the retentate sheets and adjacent filter sheets being unbonded to permit permeate contacting the retentate sheet to flow through the filter sheet to the permeate sheet, and wherein when the biomass is cellulosic biomass comprising one of wood by-products, wood fiber, plant fiber, paper and grasses, step (a) is a two-step process comprising converting the cellulosic biomass into sugar and then fermenting the sugar into ethanol.