Just to make sure we got our terms straight, Assuming the low beam headlights are already turned on with the knob at the end of the switch:
A flash to pass is sitting in the driver's seat and pulling the combination light switch lever towards you (to the back of the car) and then releasing with the lever automatically going back to the center position. While pulling towards you, the low beams should stay on and the high beams will activate as well until you let go of the lever. The low beams should not turn off during this action.
Turning on the high beams while sitting in the driver's seat is done by pushing the combination light switch lever away from you (towards the front of the car). The lever should stay in that position even when you let go of the lever. This actions turns off the low beams and turns on the high beams. In order to turn off the high beams to go back to low beams, you have to pull the lever back towards the center (resting position).
If you agree that you have tried the actions that I just described and low beams go off when you do a flash to pass then the only thing that can be wrong is the combination switch is defective. Like I mentioned earlier, the combo switch is really three switches built-in. The high-low dimmer switch portion should not be affected by a flash to pass when the low beams were on. The combo switch has a common ground going to all three internal switches. It seems like your movement of the lever breaks this ground causing the other functions to turn off / not work.
I would look for a replacement combination switch. You can get a new one online from Majestic Honda for $59.84 (plus shipping):
Honda Automotive Parts
Item number 10 (same part number for MT and CVT models)
The recall I mentioned earlier is for 00-02 Insights BUT it seems to affect low beams.
I think that it is the switch or a ground loose in the switch.
JoeCVT = Just your average CVT owner