A metal-ceramic laminar-band multi matrix composite, intended for use in oxidizing, reductive or inert media at temperatures up to 1500.div.2800.degree. C. and a method of the manufacture is provided. The composite material contains up to 85 vol. % of an oxide component, for example, yttria, zirconia, hafnia, up to 85 vol. % of a compound devoid of oxygen, such as zirconium carbide, and 15.div.75 vol. % of a refractor metal, such as tungsten, molybdenum or chromium. Each of the above mentioned components of the composite exists in the form of a plurality of curved tapes. The tapes of every component are joined with the tapes of other components forming multilayer curved band-like chips, which are randomly interlaced in a compact 3-dimensioned pattern of the chips. The novel composites have high mechanical properties, are thermal- and crack resistant, and have a good thermal-shock and oxidation-erosion resistance at temperatures of 1200.degree. C. to 2800.degree. C.