A method for the manufacture of a three-dimensional object using a refractory matrix material is provided. The method includes the additive manufacture of a green body from a powder-based refractory matrix material followed by densification via chemical vapor infiltration (CVI). The refractory matrix material can be a refractory ceramic (e.g., silicon carbide, zirconium carbide, or graphite) or a refractory metal (e.g., molybdenum or tungsten). In one embodiment, the matrix material is deposited according to a binder-jet printing process to produce a green body having a complex geometry. The CVI process increases its density, provides a hermetic seal, and yields an object with mechanical integrity. The residual binder content dissociates and is removed from the green body prior to the start of the CVI process as temperatures increase in the CVI reactor. The CVI process selective deposits a fully dense coating on all internal and external surfaces of the finished object.