The reconstruction of three-dimensional acoustically penetrable bodies from far-field data corresponding to time-harmonic plane wave incidence is studied by means of the factorization method. As usual, the problem is formulated as a linear equation whose solvability determines whether a given point is inside or outside the scatterer. The authors extend the theoretical framework of the factorization method from the inpenetrable to the penetrable scatterer case by deriving an appropriate factorization of the far-field operator and obtain an explicit formula for the characteristic function of the scatterer. The theoretical results of the factorization method for the inverse acoustic transmission problem are illustrated by numerical examples in three dimensions, where a variety of connected and disconnected scatterers are successfully reconstructed by the factorization method.