The Mark Rashid approach would be to assume that the horse thinks you want the head to go down.
For instance some action of yours like the hand on the withers is being interpreted by the horse as a signal to put the head down.
The first step in such an approach is to look at what exactly triggers the unwanted movement. Many horses learn that at the end of work, going on a long rein is the cue for them to stretch their neck forward and down. So possibly it is a relaxing of the rein contact, rather than the actual getting off?
Or taking your feet from the stirrups may have been in the past associated with the loose rein and so become a substitute cue.
Or the horse is assuming that its work is done for the time being? Whereas the horse is still working (or should be) during the period of dismount.
If you can isolate the misunderstood cue you can then either reteach the horse and get the horse to understand that the behaviour he is offering is not the one required? Or you can remove the unintentional cue from your own behaviour.
It is not possible without watching both you and the horse to give a diagnosis which will then lead to cure. But as a riding school rider I find that this approach to many problems works well.
But with both mounting and dismounting problems you really need to allow time - and take half an hour to teach the new behaviour. And rrepeat it every time you ride.
If you always need to get off in a hurry because your allotted time is over, the horse will continue to lower its head.
The horse may even think that lowering its head cues you to dismount? So you are actually rewarding the unwanted behaviour every time you dismount with the head lowered.