Recent observations show the existence of an increasing number of collimated outflows ejected by young, low-mass stars which are embedded in Hii regions. At distances of a few tens of au from the star, at least one lobe of these outflows will be shielded from the ambient ionizing radiation by the compact, high-extinction circumstellar disc. Within these shielded regions, the jets are probably mostly neutral, similar to the jets in `normal' Herbig-Haro (HH) objects. At larger distances, these jets emerge into the photoionized nebula, and start to be photoionized by the radiation from the ionizing photon source of the nebula. In this paper, we model the photoionization of an initially neutral HH jet. This process begins as an ionization front at the side of the jet, which is directed towards the ionizing star of the nebula, and progresses into the beam of the jet. There are two possible solutions. In the first solution, the jet beam becomes fully ionized through the passage of an R-type ionization front. In the second solution, the ionization front slows down enough to become a D-type front (or is already a D-type front at the point in which the jet emerges into the photoionized nebula), forming a partially ionized jet beam, with an expanding photoionized region and a compressed neutral region. We explore these two types of solutions both analytically and numerically, and discuss the observational effects introduced by this jet photoionization process, concentrating in a region of parameter space that straddles the parameters deduced for HH 444 (the jet from V 510 Orionis).