We present single-dish and interferometric millimeter line observations of the HH 111 outflow and its driving source. The physical conditions of the core have been determined from the emission of the millimeter line of CO and its isotopomers and CS with the IRAM 30 m telescope, and the CO J=7-->6 line with the Caltech Submillimeter Observatory. The emission reveals a small condensation of cold (T=20-25 K) and dense gas [n(H2)=3x10^5 cm^-3]. The outflow has been mapped with the IRAM Plateau de Bure Interferometer (PdBI). The cold gas is distributed in a hollow cylinder surrounding the optical jet. The formation of this cavity and its kinematics are well accounted for in the frame of outflow gas entrainment by jet bow shocks. Evidence of gas acceleration is found along the cavity walls, correlated with the presence of optical bow shocks. The separation of the inner walls reaches 8"-10", which matches the transverse size of the wings in the bow shock. CSO observations of the J=7-->6 line show evidence of a high-velocity and hot gas component (T=300-1000 K) with a low filling factor. This emission probably arises from shocked gas in the jet. Observations of the 3P2-3P1 [CI] line are consistent with C-type nondissociative shocks. Mapping of the high-velocity molecular bullets B1-B3, located beyond the optical jet, reveals small structures of 3" x 7" flattened perpendicular to the flow direction. They are made of cold (T ~ 30K), moderate density gas [n(H2) = (0.5-1.0)x10^4 cm^-3], expanding into the low-density surrounding medium. Their properties are consistent with their being shocked gas knots resulting from past time-variable ejections in the jet.Peer reviewed