Light aircraft Flight Instructor pilot an NMAC with a commercial jet departing OAK.

Narrative

We requested transition through HWD on our way to OAK. We were told 'northwest transition approved; fly 1300 ft.' We noted a jet taking the field 28L just below and to our right. Our course of flight was set to cross the field towards the end of the 28L. About midfield Tower told us to descend 1300 ft.; he was showing us at 1400 ft. The jet lifted off just after this call and began its climb out. I instructed my student to turn left to avoid crossing over the runway as we appeared to be on course to collide with the jet's straight out departure.Seconds after my instruction; Tower told us to 'cross overhead midfield. Cross overhead.' We complied however it was questionable to do so considering how close we passed with the jet. I think Tower should have had us fly parallel to the field and allowed the jet adequate space to take off and then had us cross. After landing we discussed the event and what we would have done differently. Upon seeing the jet take the runway; we would have contacted Tower to verify our position; identify the jet taking the runway and ask exactly where Tower wanted us to cross the field with relation to the jet taking off.