HH 444 is a stellar jet which is immersed in the H II region photoionized by sigma Orionis. Spatially resolved, high spectral resolution observations of the Hα and [N II] lambda lambda 6548, 6584 lines have been obtained for this object. These observations reveal for the first time the detailed velocity structure of the stellar jet and its associated bow-shock. The line profiles are modeled with gasdynamic numerical simulations, using a 3D code that also includes the transfer of the ionizing radiation from an external source (i.e., sigma Orionis for the case of HH 444). In order to reproduce the observed characteristics of the line profiles, we find that an axially peaked initial velocity profile for the jet and a non-zero initial opening angle for the flow with a time-variable ejection velocity is required. With these three ingredients we can reproduce the observed ``acceleration'' of the material along the jet beam, the rapid Hα intensity drop for increasing distances from the source, and the knotty structure of the jet, respectively.